rajeev.apm's picture
Dr. Rajeev
Associate Professor
Department of Mathematical Sciences,IIT BHU.
rajeev.apm@iitbhu.ac.in
+91 9451941396
Area of Interest: 
Mathematical Modelling, Moving Boundary Problems

  • Ph. D. in Applied Mathematics, IIT (BHU)  in 2009
  • M. Sc. in Mathematics, Banaras Hindu University (2004)
  • B. Sc. in Mathematics (Honours), Banaras Hindu University (2002)
  • Associate Professor in Department of Mathematical Sciences, Indian Institute of Technology (BHU) Varanasi:  July 19, 2017-till date.
  • Assistant Professor (Mathematics) in the Department of Mathematical Sciences, IIT (BHU), Varanasi from 30-10-2007 to July 18, 2017. 
  • Assistant Professor (Mathematics) in the Department/ Faculty of Commerce, BHU, Varanasi from 10-07-2006 to 30-10-2007.  

Courses Taught at Indian Institute of Technology (BHU)

  • Engineering Mathematics I
  • Mathematical Methods
  • Numerical Techniques
  • Finite Element Method
  • Rajeev, K.N. Rai, S. Das, Numerical solution of a moving-boundary problem with variable latent heat, Int. J. Heat and Mass Transfer 52 (2009) 1913–1917. 
  • Rajeev, K. N. Rai, and S. Das, Solution of one-dimensional moving boundary problem with periodic boundary condition by variational iteration method, Thermal Science, 13 (2009), pp. 199-204. 
  • S. Das, P.K. Gupta and Rajeev, A fractional predator- prey model and its solution,   Int. J. Non-linear Sci. and Numerical Simulation, 10 (2009), pp. 873-876. 
  • Rajeev and S Das,   A numerical study for inward solidification of a liquid contain in cylindrical and spherical vessel, Thermal Science, 14 (2010), pp. 365-372.
  • S. Das, Rajeev, Solution of fractional diffusion equation with a moving boundary condition by variational iteration method and Adomian decomposition method, Z. Naturforsch. 65a (2010) 793–799.  
  • S. Das and Rajeev, An approximate analytical solution of one-dimensional phase change problems in a finite domain, Applied Mathematics and Computation, 217 (2011), 6040–6046. 
  • Rajeev, M. S. Kushwaha, Homotopy perturbation method for a limit case Stefan problem governed by fractional diffusion equation, Applied Math. Modell. , 37 (2013), pp. 3589–3599.
  • Rajeev, M S Kushwaha, Ajay Kumar, An approximate solution to a moving boundary problem with space–time fractional derivative in fluvio-deltaic sedimentation process, Ain Shams Engg. J (Elsevier) 4 (2013), pp. 889–895.
  • Rajeev, Homotopy perturbation method for a Stefan problem with variable latent heat, Thermal Science 18 (2014), pp. 391-398. 
  • Rajeev, M.S. Kushwaha, A.K. Singh, A study of a Stefan problem governed with space–time fractional derivatives, Journal of Heat and Mass Transfer Research, 3 (2016), 145-151.
  • Rajeev and A.K. Singh, Homotopy analysis method for a fractional Stefan problem, Nonlinear Sci. Lett. A, 8(2017) 50-59.
  • Rajeev and A.K. Singh, A wavelet based approach to a moving boundary problem, Nonlinear Sci. Lett. A, Vol. 8, (2017), (3), pp.294-302. 
  • A K Singh, A Kumar, Rajeev, A Stefan problem with variable thermal coefficients and moving phase change material, Journal of King Saud University – Science, 31, (4), 2019, pp 1064-1069.
  • A. K. Singh, A. Kumar and Rajeev, Exact and approximate solutions of a phase change problem with moving phase change material and variable thermal coefficients. J. King Saud Univ. Sci., 31 (4), 2019, pp 1318-1325.
  • Ajay Kumar, A K Singh, Rajeev, A phase change problem including space-dependent latent heat and periodic heat flux, Nonlinear Dynamics and Systems Theory, 19 (1-SI) (2019) 178–185.
  • K. D. Dwivedi, Rajeev and S. Das, Fibonacci Collocation Method to Solve Two-dimensional Nonlinear Fractional Order Advection-Reaction Diffusion Equation, Special Topics & Reviews in Porous Media, 10 (6), 2019, pp. 569-584.
  • Rajeev and Mohan Singh Kushwaha, Comparison between Adomian decomposition method and optimal homotopy asymptotic method for a two moving boundaries problem, Differential Equations and Dynamical Systems (Springer)28,  (2020), pp. 431–446.
  •  A. Kumar, A.K. Singh, Rajeev, A Stefan problem with temperature and time dependent thermal, Journal of King Saud University – Science, 32 (1), 2020, pp 97-101.
  • KD Dwivedi, Rajeev, S Das, D Baleanu, Numerical Solution of Nonlinear Space–Time Fractional-Order Advection–Reaction–Diffusion Equation, Journal of Computational and Nonlinear Dynamics (Transactions of the ASME), 15 (6), 2020, 061005.
  • A. Kumar, A.K. Singh,  Rajeev,  A moving boundary problem with variable specific heat and thermal conductivity, Journal of King Saud University – Science,  32 (1), 2020, pp. 384-389.
  • Lipi Jain, Abhishek Kumar, Rajeev, A numerical study of a moving boundary problem with mixed boundary condition and variable thermal coefficients, Computational Thermal Sciences, 12(3), 2020,  pp. 249–260.
  • Abhishek Kumar, Rajeev, A Stefan problem with moving phase change material, variable thermal conductivity and periodic boundary condition, Applied Mathematics and Computation, 386 (2020) 125490
  • A. Kumar, A.K. Singh, Rajeev, A freezing problem with varying thermal coefficients and convective boundary condition. Int. J. Appl. Comput. Math., 6 (5) (2020), Article number: 148.
  • Abhishek Kumar, Rajeev, A moving boundary problem with space-fractional diffusion logistic population model and density-dependent dispersal rate, Applied Mathematical Modelling, 88 (2020), pp 951–965.
  • Mahesh Kumar, K.N. Rai, Rajeev, A study of fractional order dual-phase-lag bioheat transfer model, Journal of Thermal Biology , 93 (2020) 102661.
  • KD Dwivedi, Rajeev, S. Das, J F Gomez-Aguilar, Finite difference/collocation method to solve multi term variable-order fractional reaction–advection–diffusion equation in heterogeneous medium. Numerical Methods Partial Differential Eq. 2020; 1–15, https://doi.org/10.1002/num.22648.
  • Kumar, M., Rai, K.N. & Rajeev, Analysis of DPL Bioheat Transfer Model During Thermal Treatment. Int. J. Appl. Comput. Math 7, 44 (2021). https://doi.org/10.1007/s40819-021-00976-w
  • M Singh, S Das, Rajeev, EM Craciun, Numerical solution of two-dimensional nonlinear fractional order reaction-advection-diffusion equation by using collocation method, An. St. Univ. Ovidius Constanta 29 (2), 211-230, 2021.
  • Dwivedi, K.D., Rajeev Numerical Solution of Fractional Order Advection Reaction Diffusion Equation with Fibonacci Neural Network. Neural Process Letter 53, 2687–2699 (2021). https://doi.org/10.1007/s11063-021-10513-x
  • A. Kumar, V. K. Yadav, S. Das and Rajeev, "Global Exponential Stability of Takagi-Sugeno Fuzzy Cohen-Grossberg Neural Network With Time-Varying Delays," in IEEE Control Systems Letters, vol. 6, pp. 325-330, 2022, doi: 10.1109/LCSYS.2021.3073962.
  • K D Dwivedi, S Das, Rajeev, D Baleanu, Numerical solution of highly non-linear fractional order reaction advection diffusion equation using the cubic B-spline collocation method, International Journal of Nonlinear Sciences and Numerical Simulation, 2021, https://doi.org/10.1515/ijnsns-2020-0112
  • Ankit Kumar, S Das, Rajeev, V.K. Yadav, Global exponential synchronization of complex-valued recurrent neural networks in presence of uncertainty along with time-varying bounded and unbounded delay terms, Int. J. Dynam. Control (2021). https://doi.org/10.1007/s40435-021-00838-9
  • Ankit Kumar, S. Das, V.K. Yadav, Rajeev, Jinde Cao and C Huang, Synchronizations of fuzzy cellular neural networks with proportional time-delay, AIMS Mathematics, 6(10), 2021 10620–10641.  
  • Ankit Kumar, S. Das, Vijay K. Yadav, Rajeev, Global quasi-synchronization of complex-valued recurrent neural networks with time-varying delay and interaction terms, Chaos, Solitons & Fractals, 152, 2021, 111323.
  • Abhishek Kumar, Rajeev, Heat balance integral method for a time-fractional Stefan problem with Robin boundary condition and temperature-dependent thermal conductivity, Computational Thermal Sciences, 13 (6), 2021, 71–84.

Ph.D. Supervision :

  • Mr. M. S. Kushwaha (Awarded in  2015)
  • Mr. Ajay Kumar (Awarded in  2019)
  • Mr. A.K. Singh (Awarded in  2019)
  • Mr. Kushal Dhar Drivedi (Thesis submitted in 2021)
  • Mr. Abhishek Kumar (Ongoing)
  • Mr. Mahesh Kumar (Ongoing)
  • Mr. Ankit Kumar (Ongoing)
  • Mr. Manipal Singh (Ongoing)
  • Ms Rashmi Sharma (Ongoing)
  • Mr. Ankit Kumar (Ongoing) 
  • Ms Lipi Jain (Ongoing)
                                                                                                                 

M.Tech. Supervision :

  • Mr. Rahul Rajput (08412EN001), Awarded in  2013 (supervisor)
  • Ms. Purnima Lodha (09412EN006), Awarded in  2014 (supervisor)
  • Mr. Aditya Modi (09412EN008), Awarded in  2014 (supervisor)
  • Mr. Naresh Kumar Raigar (10412EN014), Awarded in  2015 (supervisor)
  • Mr. Shubham Agrawal (11412EN006), Awarded in  2016 (supervisor) 
  • Mr. Kethavath Janardhan (12412EN020) Awarded in  2017(supervisor)
  • Mr. Mayank Aharwar (13123011), Awarded in  2018 (supervisor)
  • Mr. Rishabh Dall (13123013), Awarded in  2018(supervisor)
  • Mr. Ishkaran Mangat (14123021), Awarded in  2019 (supervisor)
  • Mr. Arun Meena (13123003) Awarded in 2019 (co-supervisor)
  • Mr. Rahul Maurya (13123012) Awarded in 2019 (co-supervisor)
  • Mr. Khushal  Patidar (15123007) Awarded in 2020(supervisor)
  • Mr. Vaibhav Kumar Dixit (16123018) Awarded in 2021(supervisor)
  • Mr. Anshuman Singh (16123006) Awarded in 2021(supervisor)

     

Activities: 

  1. Treasurer in RTMMS-2010 (a National conference from March 18 - 20, 2010).
  2. Organizing Secretary and Treasurer in RTMMS-2011 (a National conference from March 25 - 27, 2011).
  3. Organizing Secretary and Treasurer in MMCS-2012 (a National Conference from March 23 - 25, 2012).
  4. Course Coordinator of AICTE sponsored QIP-Short Term Course on Advanced Numerical Schemes for Scientists & Engineers (ANSSE-19) during Aug. 12-16, 2019.
  5. Course Coordinator of a one day workshop on “Study and Analysis of Mathematical Models of Moving Boundary Problems” sponsored by Science and Engineering Research Board (SERB), Govt. of India​ on August 17, 2019​.
  6. Chair a session in 17th International Conference on Mathematical Sciences, Engineering and Applications (ICMSEA), July 4-5, 2015, Singapore.
  7. Chair a session in ICDECP19 , June 17-19, 2019 IIT Mandi.
  8. Reviewer in reputed journals.

paper presentation/invited talk/Lectures Delivered

  • National conference on recent trends in Mathematical Modeling and Simulation (RTMMS-2010) organized by Dept. of Applied Mathematics, I.T., BHU, Varanasi, March 18-20, 2010.Topic: A numerical study for a Stefan problem subject to the periodic boundary conditions.
  • National Conference on Mathematical Modeling and Computer Simulation (MMCS-2011) organized by Dept. of Applied Mathematics (Under SAP), I.T., BHU, Varanasi, March 25-27, 2011.Topic: A numerical approach for a moving boundary problem with time-dependent boundary conditions
  • National conference on Mathematical Modeling and Computer Simulation (MMCS-2012) organized by Dept. of Applied Mathematics (Under SAP), Institute of Technology, BHU Varanasi, March 23-25, 2012.Topic: An approximate solution to a moving boundary problem in fluvio-deltaic sedimentation process.
  • A talk in International Conference on Recent Advances in Pure and Applied Mathematics, ANTALYA, TURKEY, Nov 6-9, 2014. Topic:An approximate solution to a problem of two moving boundaries governed with fractional time derivative in drug release devices.
  • 17th International Conference on Mathematical sciences, Engineering and Applications (ICMSEA), 2015, Singapore, July 4-5.Topic:A Numerical Solution Based On Operational Matrix of Differentiation of Shifted Second Kind Chebyshev Wavelets for a Stefan Problem.
  •  2nd International conference on Mathematical Techniques in Engineering Applications (ICMTEA 2016), Dehradun, Uttarakhand, April 29-30, 2016.Topic: Comparison between Adomian decomposition method and optimal homotopy asymptotic method for a two moving boundaries problem.
  • International Conference on Mathematical Modelling in Applied Sciences (ICMMAS’17) during July 24-28, 2017, in Peter the Great St. Petersburg Polytechnic University, Russia. Topic: A numerical solution of a moving boundary problem.
  • International Conference on Applied and Computational Mathematics (ICACM-2018) during November 23-25, 2018, IIT Kharagpur.                            Topic: A Spectral Collocation approach to a melting problem including variable thermal coefficients.
  • Invited talk in an International Conference  ICDECP19 during June 17-19, 2019, IIT Mandi. Topic: A Finite element approach to a moving boundary problem with variable thermal conductivity.
  • Guest lecture in an AICTE sponsored QIP-Short Term Course on Advanced Numerical Schemes for Scientists & Engineers (ANSSE-19) during Aug. 12-16, 2019 in the Dept of Mathematical Sciences, IIT(BHU).
  • Guest lecture in a one day workshop on “Study and Analysis of Mathematical Models of Moving Boundary Problems” sponsored by SERB, Govt. of India​ on August 17, 2019, in the Dept of Mathematical Sciences, IIT(BHU).
  • Invited talk in an International Conference on Computational Mathematics and its Applications (CMA 2019)CMA 2019 during Nov. 12-14, 2019,  IIT Indore. Topic: A phase Change Problem with variable thermal conductivity by Spectral Collocation and spectral Tau methods.
  • Warden of ASN Bose Hostel, IIT (BHU) Varanasi from 18/09/2012 to 29/05/2018.
  • Admin Warden of ASN Bose Hostel, IIT (BHU) Varanasi from 30-05-2018 to 31-05-2021.
  • Convener of the DUGC during 2017-18, Department of Mathematical Sciences, IIT(BHU) Varanasi.
  • a member of the  Departmental faculty Affairs committee (DFAC) for the  session 2019-20.
  • a member of  BoG  of Rajkiya Engineering College, Ambedkar Nagar (UP) from March 2019 till date.

1. A project of Science and Engineering Research Board (SERB) of the total cost of Rs. 2244000/- (Rs. Twenty Two Lakh Forty Four Thousand Only) for three years.
 Project No.: R&D/SERB/Math/18-19/02                   Project start date is 22-Feb-19
Topic: Study and Analysis of Mathematical Models of Moving Boundary Problems.