sudarshans@iisc.ac.in
Dr. Sudarshan Santra, Ph.D.
Post-Doctoral Fellow
Axis Bank Centre for Mathematics & Computing
Department of Computational and Data Sciences
Indian Institute of Science Bangalore
Bengaluru, Karnataka, 560012
E-mails: sudarshans@iisc.ac.in, sudsantra@gmail.com
Phone: +91 9874249522, +91 9123316375
Career
Research Interests
Post-Doc, Axis Bank PDF, Axis Bank Centre for Mathematics & Computing, Dept. CDS, IISc Bangalore
Post-Doc, Project Associate, Dept. CDS, IISc Bangalore
Ph.D., Dept. of Mathematics, NIT Rourkela
M.Sc., Dept. of Mathematics, IIT Guwahati
B.Sc., Dept. of Mathematics, University of Calcutta
Numerical Analysis
Fractional-Order Partial Differential Equations
Fractional-Order Integro-Partial Differential Equations
Wavelets in Scientific Computing
Biography
Dr. Sudarshan Santra is a distinguished mathematician whose academic and research journey has been marked by significant achievements and contributions to the field of computational mathematics. After completing his B.Sc. in Mathematics Honours from the University of Calcutta, West Bengal, he pursued an M.Sc. in Mathematics and Computing at the Indian Institute of Technology Guwahati, Assam. Here, he explored perturbation techniques for differential equations under Prof. Swaroop Nandan Bora's guidance.
Dr. Santra's quest for deeper mathematical understanding led him to the National Institute of Technology Rourkela, Odisha, where he completed his Ph.D. in Mathematics. Under the supervision of Prof. Jugal Mohapatra, he developed novel numerical techniques for solving various fractional-order differential and integro-differential equations, significantly contributing to their practical applications.
Currently, Dr. Santra is a Post-Doctoral Research Fellow in the Numerical Algorithms and Tensor Learning (NATL) Lab at the Indian Institute of Science Bangalore, Karnataka. Working under the guidance of Prof. Ratikanta Behera and supported by the Post-Doctoral Fellowship from the Axis Bank Centre for Mathematics & Computing at IISc Bangalore, he is focused on simulating finite difference techniques combined with wavelet analysis, aiming for a higher accuracy rate in computational mathematics. His ongoing research and dedication continue to make substantial impacts in the field.
Activities
Workshop on "Mathematics and Computing of Uncertainty Quantification in Model-Based Simulation for Risk-Informed Decision Making", December 14–15, 2023
It gives me great pleasure to announce that I am honored to have the opportunity to welcome honorary speaker, Dr. Sankaran Mahadevan, John R. Murray Sr. Professor, Professor of Civil and Environmental Engineering at Vanderbilt University, Nashville, US, to the workshop on "Mathematics and Computing of Uncertainty Quantification in Model-Based Simulation for Risk-Informed Decision Making," which was held on December 14–15, 2023. I am also delighted to welcome the honorary guests, Dr. G. K. Ananthasuresh, Professor, Dept. of Mechanical Engineering, IISc Bangalore, and Dr. S. Gopalakrishnan, Convenor of the Axis Bank Centre for Mathematics & Computing, IISc Bangalore. A special thanks to Dr. M. K. Raghavendra, the Program Manager, and Mr. J. Vivek Gnana Pandian, the senior Project Associate.
Workshop on "Tensor Computation and Machine Learning (TCML)", November 17-18, 2023
I'm honored to share my experience hosting the workshop on "Tensor Computation and Machine Learning (TCML)", which took place on November 17-18, 2023, organized by the Department of Computational and Data Sciences at the Indian Institute of Science, Bangalore. The workshop, focused on tensor computations and machine learning, provided an engaging platform for knowledge exchange and collaboration. Thanks to my supervisor Dr. Ratikanta Behera, the convenor of the workshop, and all the invited speakers who had shared their expertise in this workshop. Thanks to all the enthusiastic participants. The workshop, blending theory with practical insights, provided a comprehensive view of the latest developments in tensor computations and machine learning. Engaging sessions and networking opportunities with like-minded participants made the experience both enriching and collaborative.
Selected Publications
Santra, S., Mohapatra, J., Das, P. & Choudhuri, D. (2023). Higher order approximations for fractional order integro-parabolic partial differential equations on an adaptive mesh with error analysis. Computers & Mathematics with Applications. https://doi.org/10.1016/j.camwa.2023.09.008
Layer Behavior
Maximum Error
Log-log Plot
Mohapatra, J., Santra, S. & Ramos, H. (2023). Analytical and numerical solution for the time fractional Black-Scholes model under jump-diffusion. Computational Economics. https://doi.org/10.1007/s10614-023-10386-3
European Call Option
European Put Option
Solution obtained by FDM
Santra, S., & Mohapatra, J. (2022). Analysis of a finite difference method based on L1 discretization for solving multi-term fractional differential equation involving weak singularity. Mathematical Methods in the Applied Sciences, 45(11), 6677–6690. https://doi.org/10.1002/mma.8199
Initial Layer Behaviour
Global Error
Log-log Plot
Santra, S., & Mohapatra, J. (2022). A novel finite difference technique with error estimate for time fractional partial integro-differential equation of Volterra type. Journal of Computational and Applied Mathematics, 400. https://doi.org/10.1016/j.cam.2021.113746
Analytical Solution
Numerical Solution
Maximum Error
Santra, S., & Mohapatra, J. (2021). Analysis of the L1 scheme for a time fractional parabolic-elliptic problem involving weak singularity. Mathematical Methods in the Applied Sciences, 44(2), 1529–1541. https://doi.org/10.1002/mma.6850
Surface Plot
Surface Plot
Log-log Plot