Research Articles

◼️ Goswami A, Patel KS, Sahu PK (2025) A novel difference equation approach for the stability and robustness of compact schemes for variable coefficient PDEs. Computational and Applied Mathematics 44(5) 213, doi.org/10.1007/s40314-025-03142-w

◼️ Goswami A, Patel KS (2025) Domain truncation error analysis for a multidimensional system of PDEs of option prices. Mathematics and Computers in Simulation, doi.org/10.1016/j.matcom.2025.04.002

◼️ Sahu PK, Patel KS (2024) High-order accurate variable time step compact schemes for pricing vanilla and exotic options. Journal of Applied Mathematics and Computing 70(5): 4021-4052, doi.org/10.1007/s12190-024-02118-z 

◼️ Goswami A, Patel KS (2024) Estimation of domain truncation error for a system of PDEs arising in option pricing. arXiv preprint arXiv:2401.15570., doi.org/10.48550/arXiv.2401.15570

◼️ Shubham K, Tiwari V, Patel KS (2023) Predictive learning methods to price european options using ensemble model and multi-asset data. International Journal on Artificial Intelligence Tools 32(07) 2350034., doi.org/10.1142/S0218213023500343 

◼️ Sahu PK, Patel KS (2023) HIGH ORDER METHOD FOR VARIABLE COEFFICIENT INTEGRO-DIFFERENTIAL EQUATIONS AND INEQUALITIES ARISING IN OPTION PRICING. International Journal of Numerical Analysis & Modeling 20(4)., doi.org/10.4208/ijnam2023-1023   

◼️ Sahu PK, Patel KS, Behera R (2023) Three-Time Levels Compact Scheme for Pricing European Options Under Regime Switching Jump-Diffusion Models. In International Conference on Mathematics and Computing (pp. 367-378). Singapore: Springer Nature Singapore., doi.org/10.1007/978-981-99-3080-7_27   

◼️ Bose K, Shubham K, Tiwari V, Patel KS (2022) Insect image semantic segmentation and identification using unet and deeplab v3+. In ICT Infrastructure and Computing: Proceedings of ICT4SD 2022: 703-711. Singapore: Springer Nature Singapore., doi.org/10.1007/978-981-19-5331-6_71  

◼️ Goswami A, Patel KS, Sahu PK (2022) Compact schemes for variable coefficient convection-diffusion equations. CoRR.

◼️ Goswami A, Patel KS (2022) STABILITY OF CRANK-NICOLSON COMPACT SCHEME FOR CONVECTION-DIFFUSION EQUATIONS USING MATRIX METHOD. arXiv preprint arXiv:2201.05854.

◼️ Goswami A, Patel KS (2022) Stability analysis and condition number of compact scheme for convection-diffusion equations. http://arxiv.org/abs/2201.05854 

◼️ KS Patel, M Mehra (2021) Compact Finite Difference Method for Pricing European and American Options Under Jump-Diffusion Models. Communications in Computer and Information Science 1345: 91-108., doi.org/10.1007/978-981-16-4772-7_7  

◼️ Mehra M, Patel KS, Shukla A (2021) Wavelet-optimized compact finite difference method for convection–diffusion equations. International Journal of Nonlinear Sciences and Numerical Simulation 22(3-4): 353-372.,doi.org/10.1515/ijnsns-2018-0295  

◼️ Patel KS, Mehra M (2020) Fourth order compact scheme for space fractional advection–diffusion reaction equations with variable coefficients. Journal of Computational and Applied Mathematics 380 112963., doi.org/10.1016/j.cam.2020.112963   

◼️ Patel KS, Mehra M (2019). High-order compact finite difference scheme for pricing Asian option with moving boundary condition. Differential Equations and Dynamical Systems 27: 39-56., doi.org/10.1007/s12591-017-0372-8

◼️  Patel KS, Mehra M (2018)  A numerical study of Asian option with high-order compact finite difference scheme. Journal of Applied Mathematics and Computing 57: 467-491., doi.org/10.1007/s12190-017-1115-2  

◼️ Patel KS, Mehra M (2018) Fourth-order compact scheme for option pricing under the Merton’s and Kou’s jump-diffusion models. International Journal of Theoretical and Applied Finance 21(04) 1850027., doi.org/10.1142/S0219024918500279  

◼️ Patel KS (2018) Compact finite difference methods with error analysis for problems arising in option pricing (Doctoral dissertation). 

◼️ Patel KS, Mehra M (2017) Fourth-order compact finite difference scheme for American option pricing under regime-switching jump-diffusion models. International Journal of Applied and Computational Mathematics 3: 547-567., doi.org/10.1007/s40819-017-0369-6 

◼️ Mehra M, Patel KS (2017) Algorithm 986: a suite of compact finite difference schemes. ACM Transactions on Mathematical Software (TOMS) 44(2): 1-31.,doi.org/10.1145/3119905  

◼️ Patel KS, Mehra M (2015) High-order compact finite difference method for Black–Scholes PDE. In Mathematical Analysis and its Applications: Roorkee, India, December (2014) 393-403, Springer India., doi.org/10.1007/978-81-322-2485-3_32  

Project

▪️ Global Initiative of Academic Networks (GIAN) Course: Introduction to Mathematical Finance, Course Coordinator: Kuldip Singh Patel, Foreign Faculty: Prof. Ludger Overbeck, Justus Liebig University, Germany, September 2025.

▪️ NBHM Research Project: Theoretical and data driven fair pricing of American style exotic options in regime switching market model and computations, PI: Kuldip Singh Patel, Co-PI: Dr. Anindya Goswami (IISER Pune), October 2023- October 2026.

▪️ Theory and Computation of Option Price & Optimal Portfolio Under Regime Switching Market Models” Funded by DST & DAAD, June 2021-May 2023. PI from India: Dr. Anindya Goswami (IISER Pune) Co-PI: Kuldip Singh Patel, German PI: Prof. Thomas Kruse, Justus Liebig University, Germany.

Fellowship

•Received SERB International Research Experience Fellowship (Awarded in May 2022): To visit the University of Mauritius, Mauritius, to collaborate with Prof Muddun Bhuruth for 4 months on “High-Order Compact Schemes for Pricing Interest Rate Derivatives.