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| Research Areas |
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- Numerical Analysis, Scientific Computing
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| Courses taught at IITP |
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- MA430 Numerical Analysis (M.Sc.)
- MA504 Computational Differential Equations (M.Tech. & Ph.D.)
- MA594 Seminar (M. Tech.)
- MA429 Ordinary Differential Equations (M.Sc.)
- MA523 Partial Differential Equations (M.Sc. & Ph.D.)
- MA424 Complex Analysis (M. Sc.)
- MA428 Measure Theory (M. Sc.)
- MA201 Complex Analysis & Partial Differential Equations (B.Tech.)
- MA101 Mathematics I (B. Tech.)
- MA001 Preparatory Mathematics (B. Tech.)
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| Professional Experiences |
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- Visiting Faculty (IISER Bhopal)
- Einstein Foundation Fellow (Technische Universitat, Berlin, Germany)
- NBHM Postdoctoral Fellow (IISC Bangalore)
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| Administrative Experiences |
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- Faculty Advisor, B. Tech.- M. Tech. Dual Degree students, 2023- continuing, IIT Patna
- Professor in Charge, NSO, 2021- 2023, IIT Patna
- Faculty Advisor, M.Sc. students, 2017- 2022, IIT Patna
- DAPC Member, Purchase and faculty shortlisting Committees
- TEQIP (Academic Coordinator), 2018- continuing, IIT Patna
- Department Time Table Coordinator, 2017- 2023, IIT Patna
- Departmental in Charge, Library, IIT Patna, 2016-2019
- Vice chairman, Sports, 2016-'17, IIT Patna
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| Awards & Honors |
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- Listed in Top 2% Researcher in World, published by Stanford University, 2021, 2022, 2023
- Expert Exhibit Committee Member, APJ Abdul Kalam Science City,Department of Science & Technology, Govt of Bihar
- 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
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| Member of Professional bodies |
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- Indian Mathematical Society
- Society of Industrial and Applied Mathematics
- American Mathematical Society
- Indian Science Congress Association
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| Book |
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- P. Das, Simulations of Hamilton-Jacobi Equation with Application on Finance, 2011, Lambert Academic publishing, ISBN: 978-3659358357.
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| Project |
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- P. Das, Parameter uniform numerical analysis for singularly perturbed differential equations based on mesh adaptivity, Early Career Research Award, Science & Engineering Research Board (SERB), Govt. of India. (2018-2021 extn), completed.
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| Students |
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- Ph. D. Student
- - Subrata Rana- (Ph.D. completed, single handed-ly)
- - Shridhar Kumar
- M. Tech. (Maths & Computing)
- - Abhra Dev Boral- 2021-'22
- M. Sc. Student
- - Subhankar Dhara - 2023-'24
- - Rohit Kumar Mondal - 2023-'24
- - Nilotpal Chandra - 2023-'24
- - Deepa Pandey- 2022-'23
- - Satish Kumar- 2021-'23
- - Ajay Kumar- 2021-'22
- - Deepanshi Kumari 2020-'21
- - Snehamoy Kabiraj- 2017-'18
- - Shridhar Kumar Sharma- 2018-`19
- Student
- - Nabgopal Mondal
- - Shridhar Kumar
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| Publications |
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Journal Publications:
- R. Shiromani, V. Shanthi, P. Das, A higher order hybrid-numerical approximation for a class of singularly perturbed two-dimensional convection-diffusion elliptic problem with non-smooth convection and source terms, Computers & Mathematics with Applications, 142, 9-30, doi.org/10.1016/j.camwa.2023.04.004, Elsevier, 2023, ISSN No:0898-1221.
- S. Saini, P. Das, S. Kumar, Parameter uniform higher order numerical treatment for singularly perturbed Robin type parabolic reaction diffusion multiple scale problems with large delay in time, Applied Numerical Mathematics, 196, 1-21, https://doi.org/10.1016/j.apnum.2023.10.003, Elsevier, 2024, ISSN No: 0168-9274.
- S. Saini, P. Das, and S. Kumar, Computational cost reduction for coupled system of multiple scale reaction diffusion problems with mixed type boundary conditions having boundary layers, Revista de la Real Academia de Ciencias Exactas, Fsicas y Naturales. Serie A. Matematicas, 117 (66), Paper No. 66, 27 pp., https://link.springer.com/article/10.1007/s13398-023-01397-8, Springer, 2023, ISSN No:1578-7303.
- S. Santra, J. Mohapatra, P. Das, D. Choudhuri, Higher order approximations for fractional order integro-parabolic partial differential equations on an adaptive mesh with error analysis, Computers & Mathematics with Applications, 150, 87-101, https://doi.org/10.1016/j.camwa.2023.09.008, Elsevier, 2023, ISSN No: 0898-1221
- R Choudhary, S Singh, P Das, D Kumar, A higher-order stable numerical approximation for time-fractional non-linear Kuramoto-Sivashinsky equation based on quintic B-spline, Mathematical Methods in the Applied Sciences, https://doi.org/10.1002/mma.9778,Wiley, 2023, ISSN No:1578-7303..
- H. M. Srivastava, A. K. Nain, R. K. Vats, P. Das, A theoretical study of the fractional-order p-Laplacian nonlinear Hadamard type turbulent flow models having the Ulam-Hyers stability, Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas, doi: 10.1007/s13398-023-01488-6, 117:160, Springer, 2023, ISSN No:1578-7303.
- P. Das, S. Rana and H. Ramos, On the approximate solutions of a class of fractional order nonlinear Volterra integro-diff erential initial value problems and boundary value problems of fi rst kind and their convergence analysis, Journal of Computational and Applied Mathematics, 404, 113116, Elsevier, 2022, ISSN No:0377-0427.
- K. Kumar, P. P. Chakrabarty, P. Das, H. Ramos, A graded mesh refinement approach for boundary layer originated singularly perturbed time-delayed parabolic convection diffusion problems, Mathematical Methods in the Applied Sciences,http://doi.org/10.1002/mma.7358, Wiley, 2021, ISSN No: 0170-4214.
- P. Das, S. Rana, Theoretical prospects of the solutions of fractional order weakly singular Volterra integro differential equations and their approximations with convergence analysis, Mathematical Methods in the Applied Sciences,http://doi.org/10.1002/mma.7369, Wiley, 2021, ISSN No: 0170-4214.
- D. Shakti, J. Mohapatra, P. Das and J. Vigo-Aguiar, A moving mesh refinement based optimal accurate uniformly convergent computational method for a parabolic system of boundary layer originated reaction diffusion problems with arbitrary small diffusion terms, Journal of Computational and Applied Mathematics, Elsevier, 2020, ISSN No:0377-0427,https://doi.org/10.1016/j.cam.2020.113167.
- 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, 148, 79-97, Elsevier, 2020, .
- 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,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,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.
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| Conference Publications |
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- 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.
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| Conference Presentations |
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- 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
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