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DEVELOPMENT AND ANALYSIS OF VARIABLE STEP-SIZE INTEGRATORS WITH HYBRID AND BLOCK STRUCTURES USING OPTIMAL OFF-STEP POINTS FOR INTEGRATING INITIAL VALUE ORDINARY DIFFERENTIAL SYSTEMS
Research Summary:
My research focuses on the advancement of numerical methods for solving first- and second-order initial value problems (IVPs), a critical area of numerical analysis where real-world differential systems often elude analytical solutions. Traditional techniques, including Runge-Kutta and linear multistep methods, are widely utilized but inherently constrained. The Dahlquist barrier limits the order of accuracy for linear multistep methods, while the one-step nature of Runge-Kutta approaches can result in substantial computational demands. To transcend these challenges, I have developed innovative hybrid and block methods that synergistically combine the strengths of both approaches. These methods significantly enhance computational efficiency and accuracy by evaluating multiple solution points simultaneously, effectively overcoming traditional limitations. By integrating error-controlled, variable step-size algorithms, my methodologies without incurring any additional computational cost, optimize accuracy for systems with varying complexities, all while providing an expansive stability region that facilitates the robust handling of stiff ODEs—especially in large-scale applications."
Publications
Publications
Journal Publications:
Rajat Singla, Gurjinder Singh, Vinay Kanwar, Higinio Ramos, "An Efficient optimized adaptive step-size hybrid block method for integrating $w''=f(t,w,w')$ directly," Journal of Computation and Applied Mathematics (Elsevier). SCIE (Impact Factor: 2.872) https://doi.org/10.1016/j.cam.2022.114838 (.pdf)
Rajat Singla, Gurjinder Singh, Vinay Kanwar, Higinio Ramos, "Efficient adaptive step-size formulation of an optimized two-step hybrid block method for directly solving general second-order initial-value problems," Comp. and Applied Mathematics (Springer), vol.40 (220), pp.1-13, Aug 2021. SCIE (Impact Factor: 2.99) https://doi.org/10.1007/s40314-021-01599-z (.pdf)
Rajat Singla, Gurjinder Singh, Higinio Ramos, Vinay Kanwar, "Development of a Higher-Order $\mathcal{A}$-Stable Block Approach with Symmetric Hybrid Points and an Adaptive Step-Size Strategy for Integrating Differential Systems Efficiently," Symmetry (MDPI), vol. 15 (9), pp. 1635, Aug 2023. SCIE (Impact Factor: 2.7) https://doi.org/10.3390/sym15091635 (.pdf)
Rajat Singla, Gurjinder Singh, Vinay Kanwar, Higinio Ramos, "A family of A-stable optimized hybrid block methods for integrating stiff differential systems," Mathematical Prob. in Engg. (Hindawi), vol. (2022), article id: 5576891, pp. 1-18, May 2022. SCIE (Impact Factor: 1.305) https://doi.org/10.1155/2022/5576891 (.pdf)
Gurjinder Singh, Arvind Garg, Rajat Singla, and Vinay Kanwar, "A novel two-parameter class of optimized hybrid block methods for integrating differential systems numerically," Comp. and Math Methods (Wiley Publications), vol.3 (6), pp.1-17, Nov 2021. WOS, ESCI https://doi.org/10.1002/cmm4.1214 (.pdf)
Conference Publications:
Rajat Singla, Gurjinder Singh, and Vinay Kanwar, "An adaptive step-size optimized seventh order hybrid block method for integrating differential systems efficiently," Springer Proceedings in Mathematics & Statistics 410 (2022). Int'l Conf. on Frontiers in Industrial and Applied Mathematics (FIAM-2021). SCOPUS (Impact Factor: 0.4) https://doi.org/10.1007/978-981-19-7272-0_34 (.pdf)
Rajat Singla, Gurjinder Singh, and Vinay Kanwar, "Seventh Order A-Stable Optimized Hybrid Block Method Using Adaptive Step-Size for Solving Differential Systems," AIP Conference Proceedings 2451, 020078 (2022). Int'l Conf. on Advances in Multi-Disciplinary Sciences and Engineering Research (ICAMSER-2021). SCOPUS (Impact Factor: 0.4) https://doi.org/10.1063/5.0095188 (.pdf)
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