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Dr. Vineet Kumar Singh

Professor
Department of Mathematical Sciences, IIT BHU
Phone No(s): +91-7376716701
Email: vksingh.mat@iitbhu.ac.in
Area of Interest: Numerical Analysis, Computational Methods for Integral and Differential Equations, Fractional Calculus, Mathematical Biology, Operational Matrix based Methods
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Dr. Vineet Kumar Singh is a Professor in the Department of Mathematical Sciences at IIT (BHU), Varanasi. With over 15 years of academic and research experience, Prof. Singh has established himself as an expert in Numerical Analysis, Computational Methods for Integral and Differential Equations, Fractional Calculus, Mathematical Biology, Operational Matrix based Methods. He completed his PhD from Department of Applied Mathematics, Institute of Technology (BHU) in 2009 focusing on Wavelets Based Techniques to Compute Hankel Transform and Operational Matrix Method for Abel’s Inversion and Certain Variational Problems , after earning his M.Sc. and B.Sc. degrees in Mathematics from Udai Pratap Autonomous College, Varanasi, showcasing his dedication to advancing applied mathematics.A recipient of prestigious awards like the INSA Bilateral Exchange Fellowship and the BOYSCAST Fellowship. His work continues to inspire both students and fellow researchers, making significant strides in both academic and practical domains of mathematics.

Prof. Singh has been entrusted with significant administrative responsibilities, including being President of the Faculty Forum (2024) at IIT (BHU). In this capacity, he actively promotes democratic governance and advocates for freedom of thought, expression, and action, ensuring a collaborative and inclusive environment for faculty and staff.

Google Scholar: https://scholar.google.co.in/citations?user=apxFqmIAAAAJ&hl=en

Current Position: 

Professor in Department of Mathematical Sciences, Indian Institute of Technology (BHU) Varanasi.

Academic Backgrounds:

Ph.D. :  Department of Mathematical Sciences, Indian Institute of Technology (Banaras Hindu University) Varanasi, Jan 2006- 2009

Supervisor`s Name: Prof. O. P Singh

Thesis title: Wavelets Based Techniques to Compute Hankel Transform and Operational Matrix Method for Abel’s Inversion and Certain Variational Problems

M. Sc. Mathematics, Udai Pratap Autonomous College, Varanasi, 2003.

B.Sc. Mathematics, Udai Pratap Autonomous College, Varanasi, 2001.

Postdoctoral Research Experience: 

Post-Doc Fellow ( BOYSCAST Fellow awarded by Department of  Science and Technology, India)  : Kursk State University, Kursk, Russia.

Teaching Experience: 

  • Professor, Indian Institute of Technology (BHU), Varanasi, 2024-Till Date.
  • Associate Professor, Indian Institute of Technology (BHU), Varanasi, 2017-2024.
  • Assistant Professor, Indian Institute of Technology (BHU), Varanasi, 2013-2017.
  • Assistant Professor, National Institute of Technology, Kurukshetra, 2013.
  • Assistant Professor, Birla Institute of Technology and Science, Pilani-Goa, 2009-2013.
  • Post-Doc Fellow, Kursk State University, Kursk, Russia, 2011-2012.

 

Courses Taught at Indian Institute of Technology (BHU) Varanasi:

  • MA -101: Engineering Mathematics-I
  • MA- 102: Engineering Mathematics II
  • MA- 201: Numerical Techniques
  • MA- 203: Mathematical Methods
  • MA- 312: Differential Equations
  • MA- 111: Algebra
  • MA- 311: Linear Algebra
  • Integral Equations and Calculus of Variation
  • Human Values

 

Research Areas:

  • Numerical Analysis
  • Computational Approach for Integral Equations and  Differential Equations.
  • Numerical Wavelets Analysis 
  • Operational Matrix Methods.
  • Computational Approach for Fractional Mathematical Models
  • Signal Processing by Using Wavelets

International Publications:

 Published International Papers: 67

  1. Aman Singh, Vineet Kumar Singh, Computational techniques for non linear weakly singular two dimension Volterra integral equations with combined Logarithmic kernel: Analytical and computational consideration-II, The Journal of Analysis, Accepted- January- 2025.
  2. Anatoly A. Alikhanov, Poonam Yadav, Vineet Kumar Singh, Mohammad Shahbazi Asl, A higher order compact difference scheme for mult-term time-fractional Sobolev type convection-diffusion equation, Computational and Applied Mathematics, Vol. 44, Accepted- December -2024. https://doi.org/10.1007/s40314-024-03077-8
  3. Eugene B. Postnikov, Anant Pratap Singh, Alexander V. Sychev, Anastasia I. Lavrova, Vineet Kumar Singh, A stochastic model for the bacterial growth exhibiting staged growth,desynchronization, saturation and persistence, Mathematical Bioscience, Vol. 378, Accepted- December 2024. https://doi.org/10.1016/j.mbs.2024.109322
  4. Priyanka Rajput, Nikhil Srivastava, Vineet Kumar Singh, Higher order stable numerical algorithm for the variable order time fractional sub-diffusion equation, Iranian Journal of Science, 2024. https://doi.org/10.1007/s40995-024-01726-5
  5. Aman Singh, Nikhil Srivastava, Yashveer Kumar, Vineet Kumar Singh, Computational Approach for Two-Dimensional Fractional Integro-Differential Equations, International Journal of Applied and Computational Mathematics,Vol. 10, 155, 2024. https://doi.org/10.1007/s40819-024-01785-7
  6. Sunil Kumar, Poonam Yadav, Vineet Kumar Singh, Product Integration Techniques for Fractional Integro-Differential Equations, Mathematical Methods in the Applied Sciences, 2024. https://doi.org/10.1002/mma.10464
  7. Anant Pratap Singh, Priyanka Rajput,Rahul Kumar Maurya, Vineet Kumar Singh, High Order Stable Numerical Algorithms for Generalized Time-Fractional Deterministic and Stochastic Telegraph Models, Computational and Applied Mathematics, Vol.43, 401, 2024. https://doi.org/10.1007/s40314-024-02900-6
  8. Rahul Kumar Maurya, Dongxia Li, Anant Pratap Singh, Vineet Kumar Singh, Numerical algorithm for a general fractional diffusion equation, Mathematics and Computers in Simulation, Vol. 223, 405-432, 2024. https://doi.org/10.1016/j.matcom.2024.04.018
  9. Nikki Kedia, Anatoly Alikhanov, Vineet Kumar Singh,Higher order computational approach for generalized time-fractional diffusion equation, Communications on Applied Mathematics and Computation, Published- 2024. https://doi.org/10.1007/s42967-024-00393-y
  10. Aman Singh, Eugene B. Postnikov, Poonam Yadav, Vineet Kumar Singh, Weakly singular Volterra integral equation with combined logarithmic-power-law kernel: Analytical and computational consideration, Applied Numerical Mathematics, Vol.197,164-185, 2024. https://doi.org/10.1016/j.apnum.2023.11.006
  11. Nikki Kedia, Anatoly A. Alikhanov, Vineet Kumar Singh, Robust finite difference scheme for the non-linear generalized time-fractional diffusion equation with non-smooth solution, Mathematics and Computers in Simulation, Vol.219, 337-354, 2024. https://doi.org/10.1016/j.matcom.2023.12.034
  12. Vinita Devi, Rahul Kumar Maurya, Vineet Kumar Singh, A stable operational matrix based computational approach for multi-term fractional wave model arise in a dielectric medium, Chinese Journal of Physics, Vol. 87, 556-577, 2023. https://doi.org/10.1016/j.cjph.2023.12.019 
  13. Priyanka Rajput, Nikhil Srivastava, Vineet Kumar Singh, A high order numerical method for the variable order time-fractional reaction-subdiffusion equation,Chinese Journal of Physics, Vol.85, 431-444, 2023. https://doi.org/10.1016/j.cjph.2023.07.002
  14. Poonam Yadav, Vineet Kumar Singh, Computational Techniques for the Advection-Dispersion Variable Order Model, International Journal of Computational Methods, Vol. 20, No. 10, 2350012, 2023. https://doi.org/10.1142/S0219876223500123
  15. Anant Pratap Singh, Rahul Kumar Maurya, Vineet Kumar Singh, Analysis of a robust implicit scheme for space-time fractional stochastic non-linear diffusion wave model, International Journal of Computer Mathematics, Vol.100(7), 1625-1645, 2023. https://doi.org/10.1080/00207160.2023.2207677
  16. Yashveer Kumar, Poonam Yadav, Vineet Kumar Singh, Distributed Order Gauss-Quadrature Scheme for Distributed Order Fractional Sub-Diffusion Model, Chaos, Solitons and Fractals, Vol.170,113358, 2023. https://doi.org/10.1016/j.chaos.2023.113358
  17. Yashveer Kumar, Nikhil Srivastava, Aman Singh, Vineet Kumar Singh, Wavelets Based Computational Algorithms for Multidimensional Distributed Order Fractional Differential Equations with Nonlinear Source Term, Computers and Mathematics with Applications, Vol. 132, 73-103, 2023. https://doi.org/10.1016/j.camwa.2022.12.001
  18. N. Srivastava , Vineet Kumar Singh, L3 approximation for Caputo derivative and its application to time-fractional wave equation-(I),Mathematics and Computers in Simulation, Vol.205, Pages 532-557,  2023. https://doi.org/10.1016/j.matcom.2022.10.003V. K. Singh, O. P. Singh, R. K. Pandey, Efficient algorithms to compute Hankel transform using wavelets,Computer Physics Communications, Vol.179, 812-818, 2008.https://doi.org/10.1016/j.cpc.2008.07.005
  19. Poonam Yadav, B. P. Singh, Anatoly  A. Alikhanov, Vineet Kumar Singh , Numerical scheme with convergence analysis and error estimate for variable order weakly singular integro-differential equation, International Journal of Computational Methods, Vol. 20, No. 02, 2250046, 2023. https://doi.org/10.1142/S0219876222500463
  20. Rahul Kumar Maurya, Vineet Singh, A high order adaptive numerical algorithm for fractional diffusion wave equation on non-uniform meshes, Numerical Algorithms, Vol.92, 1905-1950, 2022. https://doi.org/10.1007/s11075-022-01372-1
  21. Nikhil Srivastava, Aman Singh, Vineet Singh, Computational algorithm for financial mathematical model based on European option, Vol. 17, 467-490, 2022. Mathematical Sciences,2022. https://doi.org/10.1007/s40096-022-00474-0V. K. Singh, O. P. Singh, R. K. Pandey, Numerical evaluation of Hankel transforms by using linear Legendre multi-wavelets, Computer Physics Communications,Vol.179, 424-429,2008.https://doi.org/10.1016/j.cpc.2008.04.006
  22. Aman Singh, Nikhil Srivastava, Somveer Singh, Vineet Kumar Singh, Computational technique for multi-dimensional non-linear weakly singular fractional integro-differential equation, Chinese Journal of Physics, Vol. 80, 305-333, 2022. https://doi.org/10.1016/j.cjph.2022.04.015
  23. Kedia, N., Alikhanov, A.A., Vineet Kr. Singh, Numerical Methods for Solving the Robin Boundary Value Problem for a Generalized Diffusion Equation with a Non-smooth Solution, Mathematics and its Applications in New Computer Systems. MANCS 2021. Lecture Notes in Networks and Systems, Vol.424, 219-228, 2022. https://doi.org/10.1007/978-3-030-97020-8_20
  24. Nikki Kedia, Anatoly Alikhanov, Vineet Kumar Singh, Stable Numerical Schemes for Time-Fractional Diffusion Equation with Generalized Memory Kernel, Applied Numerical Mathematics, Vol.172, Pages 546-565, 2022. https://doi.org/10.1016/j.apnum.2021.11.006
  25. Yashveer Kumar, Vineet Kumar Singh, Computational approach based on wavelets for financial mathematical model governed by distributed order time-fractional partial differential equation, Mathematics and Computers in Simulation, Vol.190, Pages 531-569, 2021. https://doi.org/10.1016/j.matcom.2021.05.026
  26. Nikhil Srivastavam, Aman Singh, Yashveer Kumar, Vineet Kumar Singh, Efficient numerical algorithms for Riesz-space fractional partial differential equations based on finite difference/operational matrix, Applied Numerical Mathematics, Vol.161, 244-274, 2021. https://doi.org/10.1016/j.apnum.2020.10.032
  27. Vijay Kumar Patel, Somveer Singh, Vineet Kumar Singh, Numerical wavelets schemes to complex partial differential equations arising from Morlet continuous wavelet transform, Numerical Methods for Partial Differential Equations, Vol.36,1-38, 2020. https://doi.org/10.1002/num.22572
  28. Yashveer Kumar, Somveer Singh, Nikhil Srivastava, Aman Singh, Vineet Kumar Singh, Wavelet approximation scheme for distributed order fractional differential equations, Computers and Mathematics with Application, Vol.80, 1985-2017, 2020. https://doi.org/10.1016/j.camwa.2020.08.016
  29. Rahul Kumar Maurya, Vinita Devi, Vineet Kumar Singh, Stability and convergence of multistep schemes for 1D and 2D fractional model with nonlinear source term, Applied Mathematical Modeling, Vol.89, 1721-1746, 2020. https://doi.org/10.1016/j.apm.2020.08.038
  30. Rahul Kumar Maurya, Vinita Devi, Vineet Kumar Singh, Multistep schemes for one and two dimensional electromagnetic wave models based on fractional derivative approximation, Journal of Computational and Applied Mathematics, Vol.380, 112985, 2020. https://doi.org/10.1016/j.cam.2020.112985
  31. Rahul Kumar Maurya, Vinita Devi, Nikhil Srivastava, Vineet Kumar Singh, an efficient and stable Lagrangian matrix approach to Abel Integral and Integro-Differential equations, Applied Mathematics and Computation, Vol.374, 125005, 2020. https://doi.org/10.1016/j.amc.2019.125005
  32. Somveer Singh, Vinita Devi, Emran Tohidi, Vineet Kumar Singh, An efficient matrix approach for two dimensional diffusion and telegraph equations with Dirichlet boundary conditions, Physica A: Statistical Mechanics and its Applications, Vol.545, 123784, 2020. https://doi.org/10.1016/j.physa.2019.123784
  33. Vinita Devi, Rahul Kumar Maurya, Somveer Singh, Vineet Kumar Singh, Lagrange’s operational approach for the approximate solution of two-dimensional hyperbolic telegraph equation subject to Dirichlet boundary conditions, Applied Mathematics and Computation, Vol.367, 124717, 2020. https://doi.org/10.1016/j.amc.2019.124717
  34. Rahul Kumar Maurya, Vinita Devi, Vineet Kumar Singh, Lagrangian Computational Matrix Approach to Generalized Abel’s Integral Equation based on Gauss Legendre Roots, Journal of Advanced Research in Dynamical and Control Systems, Vol.11,1717-1722, 2019.
  35. Vinita Devi, Rahul Kumar Maurya, Vijay Kumar Patel, Vineet Kumar Singh, Lagrange Operational Matrix Methods to Lane-Emden, Riccati’s and Bessel’s Equations, International Journal of Applied and Computational Mathematics, 2019. doi.org/10.1007/s40819-019-0655-6. https://doi.org/10.1007/s40819-019-0655-6
  36. V. K. Patel, V. K. Singh, E. B. Postnikov, Application of Piecewise Expansion based on 2D Legendre Wavelets for Fractional Partial Differential Equation, International Journal of Pure and Applied Mathematics, Vol.119, 5159-5167, 2018. https://doi.org/10.1007/s40819-018-0560-4
  37. Vijay Kumar Patel, Somveer Singh, Vineet Kumar Singh, Emran Tohidi, Two Dimensional Wavelets Collocation Scheme for Linear and Nonlinear Volterra Weakly Singular Partial Integro-Differential Equations, International Journal of Applied and Computational Mathematics, Vol. 4: 132, 2018. https://doi.org/10.1007/s40819-018-0560-4
  38. Somveer Singh, Vijay Kumar Patel, Vineet Kumar Singh, Convergence rate of collocation method based on wavelet for nonlinear weakly singular partial integro-differential equations arising from viscoelasticity, Numerical Methods for Partial Differential Equations, Vol.34,1781-1798, 2018. https://doi.org/10.1002/num.22245
  39. Somveer Singh, Vijay Kumar Patel, Vineet Kumar Singh, Emran Tohidi, Application of Bernoulli matrix method for solving two-dimensional hyperbolic telegraph equations with Dirichlet boundary conditions, Computers and Mathematics with Applications, Vol.75, 2280-2294, 2018. https://doi.org/10.1016/j.camwa.2017.12.003
  40. S. Singh, V. K. Patel, V. K. Singh, Application of wavelet collocation method for hyperbolic partial differential equation via matrices, Applied Mathematics and Computation, Vol.320, 407–424, 2018. https://doi.org/10.1016/j.amc.2017.09.043
  41. Vijay Kumar Patel, Somveer Singh, Vineet Kumar Singh, Two-dimensional shifted Legendre polynomials collocation method for electromagnetic waves in dielectric media via almost operational matrices, Mathematical Methods in the Applied Sciences, Vol.40, 3698-3717, 2017. https://doi.org/10.1002/mma.4257
  42. Vijay Kumar Patel, Somveer Singh, Vineet Kumar Singh, Two-dimensional wavelet collocation method for electromagnetic waves in dielectric media, Journal of Computational and Applied Mathematics, Vol.317, 307–330, 2017. https://doi.org/10.1016/j.cam.2016.11.026
  43. Somveer Singh, Vijay Kumar Patel, Vineet Kumar Singh, Numerical solution of nonlinear weakly singular partial integro-differential equation via operational matrices, Applied Mathematics and Computation, Vol.298, 310–321, 2017. https://doi.org/10.1016/j.amc.2016.11.012
  44. Somveer Singh, Vijay Kumar Patel, Vineet Kumar Singh, Operational matrix approach for the solution of partial integro-differential equation, published in Applied Mathematics and Computation, Vol.283, 195-207, 2016. https://doi.org/10.1016/j.amc.2016.02.036
  45. Chandra Shekher Singh, Harendra Singh, Vineet Kumar Singh, Om P. Singh, Fractional order operational matrix methods for fractional singular integro-differential equation, Applied Mathematical Modelling, Vol.40, 10705-10718, 2016. https://doi.org/10.1016/j.apm.2016.08.011
  46. Eugene B. Postnikov, Vineet Kumar Singh, Continuous wavelet transform with the Shannon wavelet from the point of view ofhyperbolicpartial differential equations, Analysis Mathematica, Vol. 41, Issue 3, pp 199-206, 2015. https://doi.org/10.1007/s10476-015-0206-2
  47. E. B. Eugene, V.K. Singh, Local spectral analysis of images via the wavelet transform based on partial differential equations, Multidimensional system and signal analysis, Vol.25, 145-155, 2014. https://doi.org/10.1007/s11045-012-0196-1
  48. V. K. Singh, E. B. Eugene, Operational Matrix Approach for Solution of Integro-Differential Equation Arising in Theory of Anomalous Relaxation Processes in Vicinity of Singular Point, Applied Mathematical Modelling, Vol.37, 6609-6616, 2013. https://doi.org/10.1016/j.apm.2012.09.075
  49. D. Singh, R. K. Misra, V. K. Singh, R. K. Pandey, Bad data pre-filter for state estimation, Electrical power and energy systems, Vol.32, 1165-1174, 2010. https://doi.org/10.1016/j.ijepes.2010.06.016
  50. S. Dixit, V. K. Singh, A. K. Singh, O. P. Singh, Bernstein direct method for solving variational problems, International Mathematical Forum, Vol.5, No (48), 2351-2370, 2010.
  51. O. P. Singh, V. K. Singh, R. K. Pandey, An efficient and stable algorithm for   numerical evaluation of Hankel transforms, Journal of Applied Mathematics & Informatics, Vol.28 (5-6) ,1055-1071, 2010.
  52. R. K. Pandey, O. P. Singh, V. K. Singh, D. Singh,  Numerical evaluation of Hankel transforms using Haar wavelets, International Journal of Computer  Mathematics, Vol.87 (11), 2568-2573, 2010. https://doi.org/10.1080/00207160802691611
  53. R. K. Pandey, V. K. Singh, O. P. Singh, A New Stable Algorithm for Hankel transform using Chebyshev Wavelets, Communications in Computational Physics, Vol.8(2), 351-373, 2010. https://doi.org/10.4208/cicp.050609.211209a
  54. V. K. Singh, O. P. Singh, R. K. Pandey, Almost Bernstein Operational Matrix  Method For Solving Systems of Volterra Integral Equations of Convolution Type, Nonlinear Sciences Letters, Vol. A1 (2) 201-206, 2010.
  55. R. K. Pandey, O. P. Singh, V. K. Singh., A Stable Algorithm for Numerical evaluation of Hankel transforms using Haar wavelet, Numerical Algorithms,Vol.53, 451-466, 2010, https://doi.org/10.1007/s11075-009-9313-0
  56. V. K. Singh, R. K. Pandey, A Stable Algorithm for Hankel transform using hybrid of Block pulse and Legendre polynomials, Computer Physics Communications, Vol. 181, 1-10, 2010, https://doi.org/10.1016/j.cpc.2009.08.002
  57. O. P. Singh, V. K. Singh, R. K. Pandey, A  stable numerical inversion of  Abel’s integral equation using almost Bernstein operational matrix, Journal of Quantitative Spectroscopy & Radiative Transfer, Vol.111, 245-252, 2010,https://doi.org/10.1016/j.jqsrt.2009.07.007
  58. R. K. Pandey, O. P. Singh, V. K. Singh, Numerical solution of system of Volterra  integral equations using Bernstein polynomials, International Journal of  Nonlinear Sciences and Numerical Simulation Vol.10 (7) (2009) 691-695, 2009, https://doi.org/10.1515/IJNSNS.2009.10.7.891
  59. O. P. Singh, V. K. Singh, R. K. Pandey, A New Stable Algorithm for Abel   inversion Using Bernstein Polynomials, International Journal of Nonlinear  Sciences and Numerical Simulation Vol.10 (5), 681-685,  2009.https://doi.org/10.1515/IJNSNS.2009.10.5.681
  60. O. P. Singh, R. K. Pandey, V. K. Singh, An analytic algorithm for Lane –Emden  equations arising in Astrophysics using MHAM, Computer Physics Communications, Vol.180, 1116-1124, 2009.https://doi.org/10.1016/j.cpc.2009.01.012
  61. R. K. Pandey, V. K. Singh, O. P. Singh, An improved method for computing  Hankel transform, Journal of The Franklin Institute, Vol.346 102-111,2009. https://doi.org/10.1016/j.jfranklin.2008.07.002
  62. R. K. Pandey, O. P. Singh, V.K. Singh, Efficient algorithms to solve singular integral equations of Abel type, Computer & Mathematics with Applications. Vol.57(4), 664- 676, 2009. https://doi.org/10.1016/j.camwa.2008.10.085
  63. A. K. Singh, V. K. Singh, O. P. Singh, The Bernstein operational matrix of integration, Applied Mathematical Sciences, Vol. 3, 2009, no. 49, 2427-2436, 2009.
  64. R. K. Pandey, O. P. Singh, V. K. Singh, An efficient algorithm for computing zero- order Hankel transforms, Applied Mathematical Sciences Vol. 2 No.60, 2991-3000, 2008
  65. V. K. Singh, R. K. Pandey, O. P. Singh, New stable numerical solutions of  singular integral equations of Abel type by using normalized Bernstein  polynomials, Applied  Mathematical  Sciences Vol. 3 No. 5, 241-255, 2009.
  66. V. K. Singh, O. P. Singh, R. K. Pandey, Numerical evaluation of Hankel transforms by using linear Legendre multi-wavelets, Computer Physics Communications,Vol.179, 424-429,2008.https://doi.org/10.1016/j.cpc.2008.04.006
  67. V. K. Singh, O. P. Singh, R. K. Pandey, Efficient algorithms to compute Hankel transform using wavelets,Computer Physics Communications, Vol.179, 812-818, 2008.https://doi.org/10.1016/j.cpc.2008.07.005

 

Research Guidance:

Ph.D. Supervision:

SN Name of Student Thesis Title / Area of Research Status Current Position
1 Dr. Somveer Singh Numerical Methods Based on Wavelets and Operational Matrices for Partial Differential Equations and Integral Equations Awarded 2018 Lecturer Mathematics,                                      Govt. Girls Polytechnic College,              Moradabad                                                            
2 Dr. Vijay Kumar Patel Applications of Wavelets and Operational Matrices for Partial Differential Equations and Singular Integral Equations Awarded 2018

Assistant Professor, 
Vellor Institute of Technology, Bhopal
3 Dr. Vinita Devi Numerical Schemes Based on Matrix Approach for Mathematical Models with Integers and Non-Integers Orders Awarded 2020 Assistant Professor, 
Bhakt Darshan PG college jaiharikhal, Lansdowne,Uttrakhand
4 Dr. Rahul Kumar Maurya Stable Numerical Schemes adaptive Algorithms for Fractional Mathematical Models Awarded 2021

Postdoctoral Fellow,
Shanghai University, Shanghai, China                       
5 Dr. Nikhil Srivastava Approximation Techniques and Algorithms for the Fractional Order Mathematical Models Awarded 2023

 Assistant Professor,                                       National Institute of Technology Mizoram,   Mizoram-796012
6 Dr. Yashveer Kumar Numerical Schemes Based on the Operational Matrix Approach for Distributed Order Fractional Mathematical Models Awarded 2023 Postdoctoral Fellow,
INESC-ID, Tecnico, University of Lisbon,          Lisbon, Portugal
7 Dr. Aman Singh Computational Techniques and Algorithms for Integro-Differential Equations Awarded 2023  Lecturer,                                                             Govt. Polytechnic College,                       Aurangabad, Bihar- 824102
8 Dr. Nikki Kedia Stability Analysis of Approximation Techniques and Computational Algorithms for Generalized Fractional Order Mathematical Models Awarded 2023  Assistant Professor,                                           BMS Institute of Technology &   Management, Bengaluru -560064.
9 Dr. Poonam Yadav Numerical Techniques for Fractional and Variable Order Mathematical Models Awarded 2023 Temporary Faculty,                                       National Institute of Technology, Raipur
10 Dr. Anant Pratap Singh Analysis and Computational Algorithms for Deterministic and Stochastic Mathematical Models Awarded 2024

Postdoctoral Research Associate,                    Indian Institute of Technology Delhi
In Progress...
11 Priyanka Rajput Numerical Methods for Some Integral and Differential Equations Ongoing Assistant Professor,                                    Shivharsh Kisan PG College,                              Basti, UP- 272001
12 Sunil Kumar Computational Methods for Integral Equations Ongoing Research Scholar
13 Vaibhav Agrawal Stability and Synchronization Results and  Neural Networks Ongoing Research Scholar & Member of Student's Parliament
14 Shivani Gupta Adaptive Computational Approach for Reisz Fractional Advection Dispersion Wave Equations Ongoing Research Scholar
15 Vikash Sharma Numerical Methods for Stochastic Mathematical Models Ongoing Research Scholar
16 Gauri Bhadauria Computational Numerical Techniques for Integral and Differential Equations Ongoing Research Scholar
17 Akash Singh Computational Numerical Techniques for Stochastic Models Ongoing Research Scholar
18 Priyanka Computational Numerical Techniques for Fractional Models Ongoing

Research Scholar
19 Priya Singh Ongoing Project Staff

Supervised at the level of Post-doctoral

Dr. Somveer Singh joined on May 31, 2019  as National Board for Higher Mathematics (NBHM) Post-Doc fellow under my supervision.- Completed

M. Tech. Supervision (Awarded: 12):

SN Name of Student Thesis Title / Area of Research Status
1 Mr. Vipul Sharma A study on wavelet based feature extraction techniques for text independent automatic speaker verification Awarded 2015
2 Mr. Saurabh Kumar Multi-wavelet and polynomial techniques for numerical solution of integro-differential equations Awarded 2015
3 Ms. Shreya Singh Numerical methods to solve Hankel transform Awarded 2017
4 Mr. Rahul Singh Pahrwa Numerical solutions for partial differential equations Awarded 2017
5 Ms. Deeksha Kaurav Task Scheduling based on Ant Colony Optimization Awarded 2020
6 Mr. Shubham Gautam Improving Task Scheduling using Modified Generic Algorithms in Cloud Systems Awarded 2020
7 Mr. Ramanpreet Singh Gesture recognition using hybrid CNN-RNN Awarded 2021
8 Mr.Vikas Patidar Singh Fake news detection using various machine learning technique Awarded 2021
9 Ms. Apoorva Bansal Stock price prediction using LSTM Awarded 2021
10 Mr. Shubham Kumar Image Captioning Using CNN-RNN Model Awarded 2022
11 Ms. Gayatri Devi Operational Matrix Algorithms for Time Fractional Black Scholes Model Governing European Options Awarded 2024
12 Ms. Abhirami R Operational Matrix Method for Time Fractional Black Scholes Model Using Orthogonal Generating Polynomial and Interpolating Basis Functions Awarded 2024

International:

  1. Short Visit at the Euler International Mathematical Institute, Saint Petersburg, Russia, July 8-15, 2012.
  2. Short Visit at COEX, SEOUL, South Korea, 13-21 August 2014.
  3. Short Visit at Saint Petersburg Polytechnic University (SPbPU), St. Petersburg, Russia and Kursk State University, Kursk, Russia, July 24-28, 2017.
  4. Short Visit at Asian Institute of Technology. Bangkok, Thailand , June 22-24, 2018.
  5. Short visit at Department of Mathematics, Shanghai University, Shanghai, China, May 20-26, 2024.
  6. Short visit Department of Mechanical Engineering at National University of Singapore, Singapore, December 6-10, 2024.
  7. Short Visit Energy Research Institute at Nanyang Technological University (NTU), Singapore, Singapore, Dec 7-10, 2024.
  8. Short Visit to Institute of Mathematical Sciences, Universiti Malaya, Kuala Lumpur Malaysia, December 9-16, 2024.

Publications:

  1. V. K. Singh,  “Numerical wavelets method for system of singular Voltera integro-differential equation “July 8-15, 2012, International Conference on Wavelets and Applications at the Euler International Mathematical Institute, Saint Petersburg, Russia.
  2. V. K. Singh,  ” Numerical method for system of singular Voltera integro-differential equations.” August 13-21, 2014, International Congress of Mathematicians ( ICM-2014 ) , COEX, SEOUL, South Korea.
  3. S. Singh, V. K. Singh, “Application of operational matrices based on orthogonal polynomials for the numerical solution of partial differential equation” in the international conference Operator Theory, Analysis, Mathematical Physics (OTAMP)" held at St. Petersburg, Russia, August 2-7, 2016.
  4. S. Singh, V. K. Singh, “Application of operational matrices for the numerical solution of partial differential equations” in the International Conference on Mathematical Modeling and Simulation, (ICMMS-2016), held at Banaras Hindu University, Varanasi, August 29-31, 2016.
  5. S. Singh, V. K. Singh, “Application of wavelet based approximation for the solution of partial integro-differential equation arising from viscoelasticity” in the International Conference of the Indian Mathematics Consortium (TIMC) in Cooper ation with American Mathematical Society, held at Banaras Hindu University, Varanasi, December 14-17, 2016
  6. S. Singh, V. K. Singh, “Application of Chebyshev wavelet approximation for nonlinear partial differential equations arising from viscoelasticity” in the international conference “Constructive nonsmooth analysis and related topics” held at St. Petersburg, Russia, May 22-27, 2017.
  7. S. Singh, V. K. Singh, “An efficient computational technique for the numerical solution of matrix hyperbolic equations of first order” in the “International Conference on Mathematical Modeling and Applied Sciences, ICMMAS'2017” held at St. Petersburg, Russia, July 24-28, 2017.
  8. V. K. Patel, V. K. Singh, E. B. Postnikov,  "Application of piecewise expansion based on 2D Legendre wavelets for fractional partial differential equation" in the international conference on computational methods, simulation and optimization (ICCMSO-2018) held at Asian Institute of Technology. Bangkok, Thailand from June 22,  2018 to June 24, 2018.
  9. Rahul Kumar Maurya, Vineet Kumar Singh, "Adaptive Lagrangian Approach for nonlinear weakly singular partial integro -differential equation " in International Workshop on Analysis and PDE held at Leibniz University Hannover, Germany, from Oct 08-10, 2018.
  10. Vinita Devi, Vineet Kumar Singh, "Spectral Scheme for Linear and Non-Linear Initial Value Problems" in international Workshop on Analysis and PDE held at Leibniz University Hannover, Germany from Oct 08-10, 2018.
  11. Rahul Kumar Maurya, Vineet Kumar Singh "Lagrangian computational matrix approach to Generalized Abel’s Integral Equation based on Gauss-Legendre roots" in International Conference on Computational Methods, Simulation and Optimization held at Asian Institute of Technology, Bangkok, from Jan 11-13, 2019.
  12. Yashveer Kumar, Vineet Kumar Singh, “Numerical Investigation of Distributed Order Time-Fractional Black Scholes Equation”, June 01-04, 2021, SIAM Conference on Financial Mathematics and Engineering (FM21).
  13. Nikhil Srivastava, Vineet Kumar Singh, “Numerical Algorithm for Time-Fractional Black-Scholes Model in the Financial Market” Contributed talk (Virtual mode) in the SIAM Conference on Financial Mathematics and Engineering (SIAM FM-21), from June 01-04, 2021.
  14. Nikhil Srivastava, Vineet Kumar Singh, “A Novel Approximation Technique to Caputo Derivative and Its Application to Time-Fractional Diffusion Wave Problem” poster presentation (Virtual mode) in the SIAM Conference on Analysis of Partial Differential Equation (SIAM PD-22) from Mar 14-18, 2022.
  15. Yashveer Kumar, Vineet Kumar Singh, “Numerical Wavelet Tau Approximation Scheme for Distributed Order Fractional Differential Equations”, July 01-03, 2022, International Conference on Dynamical Systems, Control and their Applications, Organized by Department of Mathematics, Indian Institute of Technology Roorkee, India.
  16. Nikhil Srivastava, Vineet Kumar Singh, “Novel compact difference scheme for fractional wave equation involving Caputo derivatives” Contributed Talk (In-person) in the 9th International Conference on Computational Methods in Applied Mathematics (CMAM-2022) from Aug. 29- Sep 02, 2022 at TU Wien, Vienna, Austria.
  17. Yashveer Kumar, Vineet Kumar Singh, “Operational Matrix Approach for Distributed Order Fractional Differential Equations” October 12-14, 2022, 2nd International Conference on Applied Mathematics & Computational Sciences-2022, Organized by Department of Mathematics, DIT University, Dehradun, India.
  18. Invited speaker in ICMC (Jan 6-8, 2023) at BITS Pilani Goa Campus on L3 approximation of the Caputo fractional derivative and its applications.
  19. Invited speaker in ICDECP23 (June 15- June 17, 2023 ) at the School of Mathematical & Statistical Sciences, Indian Institute of Technology Mandi, Himachal Pradesh on Distributed order Gauss Quadrature scheme for distributed order fractional sub-diffusion model.

Administrative Experience:

SN

Designation

 Organization

Time 

Roles and Responsibilities

1

Warden

IIT(BHU),Varanasi 

2015-18

Smooth functioning of the hostel activities

2.

Member of the users committee for GRTA,

IIT(BHU),Varanasi 

2015-16

Give inputs to the Institute works committee at all stages of the project

3.

Faculty In-Charge of the institute day

IIT(BHU),Varanasi 

2016

Smooth functioning of the Institute day at Department level as well as Institute level.

4.

Member of the DUGC

IIT(BHU),Varanasi 

2016-17

Look the matter of UG students

5.

Hostel Disciplinary and Vigilance Committee

IIT(BHU),Varanasi 

2016-17

To look the issues of students/non-teaching staff in all Hostels.

6.

Member of DPGC

IIT(BHU),Varanasi 

2017-18

Look the matter of PG/PHD students

7.

Member, Faculty Forum

IIT(BHU),Varanasi 

2018-19

To promote democratic functioning of the institute in terms of freedom of thought, expression and action.

8.

Warden

IIT(BHU),Varanasi

2018-19

Smooth functioning of the hostel activities

9.

Convener, DPGC

IIT(BHU),Varanasi 

2021-22

Look the matter of PG/PHD students

10.

Member, Faculty Forum

IIT(BHU),Varanasi 

2022-23

To promote democratic functioning of the institute in terms of freedom of thought, expression and action.

11.

President Faculty Forum

IIT(BHU),Varanasi 

2023-24

To promote democratic functioning of the institute in terms of freedom of thought, expression and action.

Current Opening :

One Jrf Position : Applications are invited from highly motivated and eligible candidates for the post of JRF for the research project entitled “Adaptive computational approach for Riesz fractional advection dispersion wave equations,” funded by Science & Engineering Research Board (SERB). Last date: January 15, 2025.

Essential qualifications:
NET/GATE or equivalent as per specifications of the funding agency concerned with 55% marks (equivalent grade) in Post-Graduation/qualifying degree.
Desirable qualifications:
Sound knowledge of Applied Mathematics and Computer programming.
Application on Plain paper giving Name, permanent and correspondence address, names of father and mother, telephone no. and e-mail address, details of educational career (starting from High School or equivalent) along with self-attested copies of all mark-sheets & certificates and details of any research or other experience etc., if any, should reach within 14 days of the advertisement, to Dr. Vineet Kumar Singh, Department of Mathematical Sciences, Indian Institute of Technology (BHU), Varanasi 221 005. In addition, the candidates are requested to mail their CV's to the mail id vksingh.mat@iitbhu.ac.in.
No TA/DA will be paid if called for interview.

Post-Doc Position :

We are seeking a motivated postdoctoral researcher to join our team. Candidates with their own fellowships, such as NBHM, are encouraged to apply and should send their CV and cover letter to vksingh.mat@iitbhu.ac.in.


International Collaborators:

SN Name of Collaborators Research Areas Contact Details
1

Eugene B Postnikov

Physics of Liquids, Biophysics, Thermodynamics and Diffusion

Professor

Department of Physics and Nanotechnology,

Kursk State Technical University, Russia

Email Id: postnikov@kursksu.ru
 
2 Anatoly A. Alikhanov

Scientific Computation, Numerical Analysis and Numerical PDEs

Professor

North-Caucasus Center for Mathematical Research, North-Caucasus Federal University, Pushkin str. 1, 355017, Stavropol, Russia

Email Id: aaalikhanov@gmail.com
3

Changpin Li

Fractional Derivatives, Fractional Equations, Numerical Methods, Convection-Diffusion and Nonlinear Problems.

Professor

Department of Mathematics, Shanghai University, Shanghai 200444, China

Email Id: lcp@shu.edu.cn
4 Anastasia I. Lavrova

Theoretical Neurosciences, System biology, Dynamical Systems and Bifurcations

Professor

Saint-Petersburg State Research Institute of Phthisiopulmonology, Ligovskiy av. 2-4, Saint-Petersburg, 194064, Russia.

Email Id: aurebours@googlemail.com
5 Emran Tohidi Spectral Methods, Financial Mathematics, Optimal Control, Adaptive Numerical Methods and Bio-Mathematics

Associate Professor

Department of Mathematics, Kosar University of Bojnord, Bojnord, Iran

Email Id: etohidi110@yahoo.com