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Research Areas |
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Courses taught at IIT P |
- MA430 Numerical Analysis (M.Sc.)
- MA314 Numerical Analysis (B. Tech.)
- MA430 Computational Lab (B. Tech.)
- 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 1 (B. Tech.)
- MA002 Preparatory Mathematics 2 (B. Tech.)
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Students |
Sr. No. |
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Area of Reasearch |
Degree |
1 |
Shridhar Kumar
shridhar_2121ma11@iitp.ac.in
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Convergence Analysis of Optimal Accurate
Computational Cost Reduction Algorithms on Adaptive Meshes for One- and
Two-Dimensional Multiple Scale Coupled Systems |
PhD Synopsis over, 2024 |
2 |
Arihant Patawari
arihant_2221ma09@iitp.ac.in
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Advanced Neural Network Algorithms for Differential Models |
Registered |
3 |
Dilip Sarkar
dilip_2321ma07@iitp.ac.in
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Multiscale Analysis for Nonlinear Systems through Graph Theory |
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Former Students |
Sr. No. |
Photo |
Area of Reasearch |
Current Position |
1 |
Subrata Rana (PhD completed, 2021)
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Theory and Approximations of Singularly Perturbed and Nonlocal Integro Differential Equations
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Assistant Professor |
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Current Sponsored Projects |
Sr. No. |
Title |
Principal Investigator |
Co-Principal Investigator |
Duration |
Sponsoring Agency |
Cost |
Status |
1 |
Parameter uniform numerical analysis for singularly perturbed differential equations
based on mesh adaptivity, |
P. Das |
nil |
2018-2022 |
Early Career Research Award, Science & Engineering Research Board (SERB), Govt.
of India. |
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2 |
Numerical analysis for precipitation-dissolution type models in porous medium
with arbitrary small diffusion coefficient using time dependent mesh adaptivity,
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P. Das |
nil |
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Mathematical Research Impact Centric Support (MATRICS), Science & Engineering Research Board (SERB), Govt. of India. |
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ongoing |
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Professional Experience |
- Visiting Faculty (IISER Bhopal)
- Einstein Foundation Fellow (Technische Universitat, Berlin, Germany)
- NBHM Postdoctoral Fellow (IISC Bangalore)
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Administrative Experience |
- 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, 2016-2019, IIT Patna
- Vice chairman, Sports, 2016-'17, IIT Patna
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Awards & Honours |
- Listed in Top 2% Researcher in World, published by Stanford University, 2021, 2022, 2023, 2024
- 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 |
- Indian Mathematical Society
- Society of Industrial and Applied Mathematics
- American Mathematical Society
- Indian Science Congress Association
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Books |
- P. Das, Simulations of Hamilton-Jacobi Equation with Application on Finance, 2011, Lambert Academic publishing, ISBN: 978-3659358357.
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Publications / Journals / Conferences |
Journal Publications:
- D. Sarkar, S. Kumar, P. Das, H. Ramos Higher-order convergence analysis for interior and boundary layers originated semi-linear reaction diffusion system networked by a k-star graph with non-smooth source terms, Networks and Heterogeneous Media, 19(3): 1085–1115, 2024, https://www.aimspress.com/article/doi/10.3934/nhm.2024048, AIMS Press, 2024, ISSN No: 1556-1801.
- S Kumar, P Das, A uniformly convergent analysis for multiple scale parabolic singularly perturbed convection-diffusion coupled systems: Optimal accuracy with less computational time, Applied Numerical Mathematics, 207, 534-557, 2025, https://doi.org/10.1016/j.apnum.2024.09.020, Elsevier, ISSN No: 0168-9274.
- 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. Kumar, P. Das, K. Kumar, Adaptive mesh based efficient approximations for Darcy scale precipitation-dissolution models in porous media, International Journal for Numerical Methods in Fluids, (1D & 2D problems), 1-30, https://onlinelibrary.wiley.com/doi/epdf/10.1002/fld.5294, Wiley, 2024, ISSN No: 0271-2091.
- S. Kumar, R. Ishwariya, P. Das, Impact of mixed boundary conditions and non-smooth data on layer originated non-premixed combustion problems: Higher order convergence analysis, Studies in Applied Mathematics, https://onlinelibrary.wiley.com/doi/10.1111/sapm.12763, Wiley, 2024, ISSN No: 0022-2526.
- S. Kumar, S. Kumar, P. Das, Second order a priori and a posteriori error estimations for integral boundary value problems of nonlinear singularly perturbed parameterized form, https://link.springer.com/article/10.1007/s11075-024-01918-5, Springer, 2024, ISSN No: 1017-1398.
- 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,https://link.springer.com/article/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, https://doi.org/10.1016/j.cam.2020.113116, 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, 404, 113167, https://doi.org/10.1016/j.cam.2020.113167, Elsevier, 2022, ISSN No:0377-0427.
- 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, https://doi.org/10.1016/j.apnum.2019.08.028, 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, https://link.springer.com/article/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, https://doi.org/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, https://doi.org/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, https://doi.org/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, https://doi.org/10.1016/j.cam.2017.11.026, 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, https://link.springer.com/article/10.1007/s12591-017-0385-3, 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, https://link.springer.com/article/10.1007/s10543-015-0559-8, 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, https://doi.org/10.1016/j.cam.2015.04.034, 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 https://doi.org/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, https://doi.org/10.1016/j.amc.2014.10.023, 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, https://doi.org/10.1080/00207160.2014.902054, 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, https://link.springer.com/article/10.1007/s12190-012-0611-7, 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), https://doi.org/10.1142/S0219876212500521, 2012, World Scientific.
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Presentations |
- 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.
- 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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Invited Talks |
- "Challenges in Implementing Mathematical Knowledges into Computer", by Department of Mathematics, Kathmandu University, Nepal, at June 23, 2024.
- "A Study of Shooting Methods and Newton's Method", Invited Speaker at AESIM School" on Differential Equations, Numerical Methods and their Applications with Scientific Computing" by CIMPA & Tribhuvan University, Nepal, 12-23th June, 2024.
- "What Happens in Mathematics may not reflect inside Computer & Vice Versa", Invited Speaker at 3 Day International Workshop on Mathematical Models and Methods in Life Sciences (M³LS 2024) (Hybrid Mode) at ABV-IIITM Gwalior, 13- 15th May, 2024.
- Higher Order Numerical Analysis for Multi-term Time Fractional Partial Integro Differential Equations on Graded Meshes", Invited Speaker at International Conference on Emerging Frontiers in Nonlinear Complex Systems, Computational Intelligence, and Their Applications", VIT Chennai, 7-9th February, 2024.
- Computational Cost Reduction for Coupled System Boundary Layer Originated PDEs having Multiple Scale Nature", Invited Speaker at - Scientific Meet on Recent Trends in Applied Sciences", Physics and Applied Mathematics, Indian Statistical Institute, Kolkata, 4-5th January, 2024.
- Introduction to Fractional Di erential Equations and its Comparison with Integral Equations and Ordinary Differential Equations", Invited Speaker at - Faculty Development Program \Recent Trend in Biomathematics and Dynamical System, Bifurcation, Chaos and Numerical Methods", Mahadevananda Mahavidyalaya, Kolkata, 7-13th February, 2024.
- Numerical Consistency and Stability for Nonlinear Initial Value Problems", Faculty Development Program (FDP), Invited Speaker at - "Recent Advances in Mathematical Sciences (RAIMS)-2023", Sarala Birla University, Rachi, 6-8th November, 2023.
- Triangle and its Properties, Types of Triangles," Invited Speaker at- Instructional School for Mathematical Sciences (ISMS), 2023, at IIT Patna in collaboration with Bihar Mathematical Society, between 16th June -15th July 15, 2023.
- On the efficiency of coupled system of singularly perturbed reaction diffusion problems with mixed type boundary conditions having boundary layers" as a Keynote Speaker at- 3rd International Workshop on Numerical and Analytical Techniques in Engineering Problems, GLA University, Mathura, 22-24th June, 2023.
- "Root finding approaches- A Numerical analysis view" as an Invited Speaker, at- Ramkrishna Mission Vivekananda Centenary College, Rahara, 19-20th June, 2023.
- Problems between scientific computing and mathematics" as an Invited Speaker at- 3rd International Workshop on Numerical and Analytical Techniques in Engineering Problems, SRM Institute of Science and Technology, Chennai, 30th January- 1st February, 2023.
- Reduction of computational cost based on ADI and splitting approach for two dimensional coupled system of convection diffusion reaction problems having boundary layer phenomena" as an Invited Speaker at- 4th International conference on- "Modern Mathematical methods and High Performance Computing in Science and Technology", Motherhood University, Uttarakhand, 20-22nd December, 2022.
- Stability and consistency for nonlinear initial value problems", as an Invited Speaker at- One Week International Workshop, "Numerical Analysis of Ordinary and Fractional Partial Differential Equations", at Government Tilak PG College, Katni, Madhya Pradesh at 27-31st December, 2022.
- Height and Angle, Row Reduced Echelon Form", as an Invited Speaker at- Instructional School for Mathematical Foundation at IIT Patna in collaboration with Bihar Mathematical Society at 8-23rd October, and 5-19th November, 2022.
- Root finding approaches: A real analysis point of view", at Presidency University, Kolkata, at 6th July, 2022.
- Introduction and approximations of weakly singular Volterra integro fractional differential equations based on residual minimization method" (Virtual Mode) Universidad de Concepcion, Chile at 4th May, 2022.
- Analysis of root finding approaches", Emerging Applications of Mathematics and Statistics in Engineering Science and Technology (Virtual Mode) at NIT Rourkela, at 9-15th May, 2022.
- How to check good research journals" at Department of Mathematics, NIT Hamirpur, at 12-19th March, 2022.
- Mathematics vs Computer (via Matlab)", Workshop on software in mathematics and statistics (WSMS) (Virtual Mode) at NIT Trichy, at 6th August, 2021.
- Numerical analysis of approximate solutions for nonlinear problems with convergent & divergent experimental data", (Virtual Mode) Faculty Development Program, 17th June, 2021, Adamas University, Kolkata.
- A moving mesh algorithm based optimal accurate mesh equidistribution approach for boundary layer originated parabolic systems", (Virtual Mode) International Conference on Computational Science and Numerical Algorithms, 29-31st May, 2021, Guilin, China.
- "How to prepare for GATE Mathematics for engineering stream students" at Loknayak Jai Prakash Institute of Technology, Chapra, 24th January, 2020.
- "Geometrical way of nding solutions of rst order partial di erential equations" at Loknayak Jai Prakash Institute of Technology, Chapra, 22nd August, 2019.
- Introduction of partial differential equations and its difference with ordinary differential equations" at Darbhanga College of Engineering, Darbhanga, at 9-10th August, 2019.
- "Optimal convergent a posteriori analysis for a nonlinear system of delay differential equations with multiple layers" on "National Conference on Recent Advances in Mathematics and its Applications at National Institute of Technology, Rourkela, from 7-8th December, 2018.
- A posteriori based convergence analysis for nonlinear singularly perturbed system of delay differential equations with multiple layer phenomena" on "International Conference on Analysis and Its Applications" at National Institute of Technology, Trichy, from 2-4th July, 2018.
- "Higher order extrapolation analysis for singularly perturbed parabolic convection diffusion problems" on Recent Developments in Numerical Techniques and its Applications (RDNTA 2016)" at Department of Mathematics, National Institute of Technology, Patna, India, from 7-8th April, 2016.
- "Uniform error estimates for singularly perturbed di erential equations: A priori and a posteriori approach" on 21st August, 2015 at IISER Mohali, India.
- "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.
- "Parameter uniform error estimates for singularly perturbed differential equations on adaptive meshes" on 21st May 2013 at TIFR Bangalore
- "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
- "Fixed Point Theorems" on 3rd April 2012, at IIT Guwahati
- "From Linear towards Nonlinear Dynamics" on 9th November, 2010 at IIT Guwahati
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