Dr. Pratibhamoy Das

Research Areas:

• Numerical Analysis, Moving Mesh Methods, Singular Perturbation, A posteriori Error Estimates, r-refinement Strategy
• Ordinary and Partial Differential Equations, System of differential Equations, Integral Equations, Fractional Order Equations, Nonlinear Problems

Courses taught at IITP :

• Ordinary Differential Equations (M.Sc.)
• Partial Differential Equations (M.Sc. & Ph.D.)
• Numerical Analysis (M.Sc.)
• Computational Differential Equations (M.Tech. & Ph.D.)
• Complex Analysis & Partial Differential Equations (B.Tech.)
• Preparatory Mathematics (B. Tech.)

Professional Experience:

• Visiting Faculty (IISER Bhopal)
• Einstein Foundation Fellow (Technische Universitat, Berlin, Germany)
• NBHM Postdoctoral Fellow (IISC Bangalore)

Administrative Experience:

• Faculty Advisor, M.Sc. students, 2016- continuing, IIT Patna
• TEQIP (Academic Coordinator), 2018- continuing, IIT Patna
• Department Time Table Coordinator, 2017- continuing, IIT Patna
• Departmental in Charge, Library, IIT Patna, 2016-2019, Department of Mathematics, IIT Patna
• Vice chairman, Sports, 2016-'17, IIT Patna

Awards & Honours:

• YOUNG SCIENTIST AWARD, 100th Indian Science Congress, 2013
• EINSTEIN Foundation Program Fellowship, International Mathematical Union, Berlin, 2014
• Early Career Research Award, SERB, Govt. of India, 2018
• DAAD Research Ambassador, Germany, 2018-22
• NBHM Postdoctoral Fellowship, 2013
• NBHM Ph.D. Research Grant Award, 2010
• CSIR-NET Junior Research Fellowship 2009 All India Rank-25,
• GATE Scholarship 2008, 2009
• IIT Bombay Merit cum Mean Scholarship, 2006-2008

Member of Professional bodies:

• Society of Industrial and Applied Mathematics
• American Mathematical Society
• Indian Science Congress Association

Books:

• P. Das, Simulations of Hamilton-Jacobi Equation with Application on Finance, 2011, Lambert Academic publishing, ISBN: 978-3659358357.

Project:

• P. Das, Parameter uniform numerical analysis for singularly perturbed differential equations based on mesh adaptivity, Early Career Research Award, Science & Engineering Research Board (SERB), Project Cost- 24.4 Lakhs, Govt. of India, 2018.

Publications:

Publications journals:

• P. Das, S. Rana and J. Vigo-Aguiar, Higher order accurate approximations on equidistributed meshes for boundary layer originated mixed type reaction diffusion systems with multiple scale nature, Applied Numerical Mathematics, doi:10.1016/j.apnum.2019.08.028, Elsevier, 2019, ISSN No: 0168-9274.
• P. Das, An a posteriori based convergence analysis for a nonlinear singularly perturbed system of delay differential equations on an adaptive mesh, Numerical Algorithms, 81, 465-487, doi:10.1007/s11075-018-0557-4, Springer, 2019, ISSN No: 1017-1398.
• P. Das, S. Rana and H. Ramos, A perturbation based approach for solving fractional order Volterra-Fredholm integro differential equations and its convergence analysis, International Journal of Computer Mathematics, Taylor & Francis, doi:10.1080/00207160.2019.1673892, 2019, ISSN No:0020-7160.
• P. Das, S. Rana and H. Ramos, Homotopy Perturbation Method for Solving Caputo Type Fractional Order Volterra-Fredholm Integro-Differential Equations, Computational and Mathematical Methods, doi:10.1002/cmm4.1047, Wiley, 2019, ISSN No:2577-7408.
• M. Chandru, P. Das and H. Ramos, Numerical treatment of two-parameter singularly perturbed parabolic convection diffusion problems with non smooth data, Mathematical Methods in the Applied Sciences, 41(14), 5359-5387, https://doi.org/10.1002/mma.5067, Wiley, 2018, ISSN: 0170-4214.
• P. Das, A higher order difference method for singularly perturbed parabolic partial differential equations, Journal of Difference Equations and Applications, 24, 3, 452-477, doi:10.1080/10236198.2017.1420792, Taylor & Francis, 2018, ISSN No: 1023-6198.
• P. Das and J. Vigo-Aguiar, Parameter uniform optimal order numerical approximation of a class of singularly perturbed system of reaction diffusion problems involving a small perturbation parameter, Journal of Computational and Applied Mathematics, 354, 533-544, Elsevier, 2019, ISSN No:0377-0427.
• M. Chandru, T. Prabha, P. Das, V. Shanthi, A numerical method for solving boundary and interior layers dominated parabolic problems with discontinuous convection coefficient and source terms, Differential Equations and Dynamical Systems, 27(1-3):91-112, Springer, 2019, ISSN No:0971-3514.
• P. Das and V. Mehrmann, Numerical solution of singularly perturbed parabolic convection-diffusion- reaction problems with two small parameters, BIT Numerical Mathematics, 56, 51-76, 2016, Springer, 2016.
• P. Das, Comparison of a priori and a posteriori meshes for singularly perturbed nonlinear parameterized problems, Journal of Computational and Applied Mathematics, 290, 16-25, 2015, Elsevier.
• P. Das and V. Mehrmann, Upwind based parameter uniform convergence analysis for two parametric parabolic convection diffusion problems by moving mesh methods, Proceedings of Applied Mathematics and Mechanics, 15, 591-592 doi:10.1002/pamm.201510285, 2015, Wiley,
• P. Das and S. Natesan, Optimal error estimate using mesh equidistribution technique for singularly perturbed system of reaction-diffusion boundary value problems, Applied Mathematics and Computation., 249, 265-277, 2014, Elsevier,
• P. Das and S. Natesan, Adaptive mesh generation for singularly perturbed fourth order ordinary differential equations, International Journal of Computer Mathematics, Taylor & Francis, 92(3), 562-578, 2015,
• P. Das and S. Natesan, Numerical solution of a system of singularly perturbed convection diffusion boundary value problems using mesh equidistribution technique, Australian Journal of Mathematical Analysis and Applications, 10(1), 1-17, 2013,
• P. Das and S. Natesan, Richardson Extrapolation Method for Singularly Perturbed Convection-Diffusion Problems on Adaptively Generated Mesh, CMES Computer Modeling in Engineering Sciences, 90(6), 463-485, 2013
• P. Das and S. Natesan, A uniformly convergent hybrid scheme for singularly perturbed system of reaction-diffusion Robin type boundary value problems, Journal of Applied Mathematics and Computing, 41(1-2), 447-471, 2013, Springer.
• P. Das and S. Natesan, Higher order parameter uniform convergent schemes for Robin type reaction-diffusion problems using adaptively generated grid, International Journal of Computational Methods, 9(4), 2012, World Scientific, doi:10.1142/S0219876212500521.

Conference Publication:

• P. Das and H. Ramos, Homotopy Perturbation Method for solving fractional Volterra-Fredholm integro differential equations 18th International Conference CMMSE 2018 organized by Departmento de Mathematicas, Universidad de Cadiz, , July 9-13, 2018, Rota, Cadiz, Spain.
• P. Das and J. Vigo-Aguiar, Parameter uniform numerical approximation of the solution of a system of reaction diffusion problems involving a small perturbation parameter, 17th International Conference "Computational and Mathematical Methods in Science and Engineering (CMMSE 2017)" organized by Departmento de Mathematicas, Universidad de Cadiz, Vol: 2, Page: 704-717,July 4-8, 2017, Rota, Cadiz, Spain.
• M. Chandru, T. Prabha, P. Das, V. Shanthi and H. Ramos, An efficient numerical method for two parameter singularly perturbed problem with discontinuous convection coefficient and source term, 17th International Conference "Computational and Mathematical Methods in Science and Engineering (CMMSE 2017)" organized by Departmento de Mathematicas, Universidad de Cadiz, Vol: 2, Page: 553-562, July 4-8, 2017, Rota, Cadiz,Spain.
• P. Das and V. Mehrmann, Upwind based parameter uniform convergence analysis for two parametric parabolic convection diffusion problems by moving mesh methods, International Conference "Gesellschaft fur Angewandte Mathematik und Mechanik (GAMM-2015)" organized by International Association of Applied Mathematics and Mechanics on their 86th Annual Meeting, Universita del Salento, Page: 586-, March 23-27th 2015, Lecce,Italy.
• P. Das, S. Natesan, Parameter-uniform numerical method for a system of singularly perturbed convection-diffusion boundary-value problems on adaptively generated grid. Proceedings of the International Conference on Advances in Modeling, Optimization and Computing (AMOC-2011), IIT Roorkee, Roorkee, India, page: 779-790, December 5-7, 2011.

Conference Presentation:

• P. Das, S. Rana and J. Vigo-Aguiar, Uniformly convergent numerical methods for singularly perturbed mixed type reaction diffusion systems with boundary layers, 18th International Conference "Computational and Mathematical Methods in Science and Engineering (CMMSE 2018)" organized by Departmento de Mathematicas, Universidad de Cadiz, Vol: 2, Page:, July 9-13, 2018, Rota, Cadiz, Spain.
• International Conference on "Mathematical Analysis and Application in Modeling (ICMAAM 2018)" at Department of Mathematics, Jadavpur University, Kolkata, from 9-12th January, 2018.
• A posteriori error estimates for a class of differential algebraic equations in singular perturbation context. on “Numerical Algebra, Matrix Theory, Differential Algebraic Equations and Control Theory" at Technische Universitat, Berlin, from 6-9th May, 2015, Berlin, Germany.
• Upwind based parameter uniform convergence analysis for two parametric parabolic convection diffusion problems by moving mesh methods, International Conference “Gesellschaft fur Angewandte Mathematik und Mechanik (GAMM-2015)" organized by International Association of Applied Mathematics and Mechanics on their 86th Annual Meeting, Universita del Salento, March 23-27th 2015, Lecce, Italy.
• “A priori and a posteriori uniform error estimates based on moving meshes for singularly perturbed problems" on 23rd October 2014 at Technische Universitat, Berlin, Germany.
• “A priori and a posteriori error estimates for singularly perturbed general system of reaction-diffusion boundary-value problems using grid adaptation" at 100th Indian Science Congress on 4th January, 2013 Calcutta