Presenting at the 2026 SIAM Central States Section Annual Meeting at Jackson State University.
My research is in numerical analysis, with a focus on differential-algebraic equations (DAEs) and implicit Runge–Kutta methods. I study the accuracy, convergence, and computational properties of numerical methods for DAEs of different indices, with particular interest in constrained systems and the construction of reliable starting approximations. My work combines theoretical analysis with computational experiments.
My research statement is available upon request. Please feel free to contact me for additional materials.
Publications:
Manuscript prepared for submission:
Intrinsic Projection of Implicit Runge-Kutta Methods for semi-explicit differential-algebraic equations of index 3, by Laurent O. Jay and Nikita Kapur, manuscript prepared for submission.
Manuscripts in preparation:
Starting Approximations of Index-1 Differential Algebraic Equations and Singular Perturbation Problems, by Laurent O. Jay and Nikita Kapur, manuscript in preparation.
Randomized FEAST Algorithm for Generalized Hermitian Eigenvalue Problems with Probabilistic Error Analysis, by Nikita Kapur, Agnieszka Miedlar, Arvind K. Saibaba, and Eric de Sturler, manuscript in preparation.
Conference Talks:
Intrinsic Projection of Implicit Runge-Kutta Methods for Index-3 Differential-Algebraic Equations, SIAM Central States Section Annual Meeting, Jackson State University, Mississippi, October 2026.
Intrinsic Projection of Implicit Runge-Kutta Methods for Index-3 Differential-Algebraic Equations, SIAM New England Section Annual Meeting, University of Massachusetts, Dartmouth, August 2026.
Intrinsic Projection of Implicit Runge-Kutta Methods for Differential-Algebraic Equations, SIAM Central States Section Annual Meeting, University of Missouri, Kansas City, October 2024.
Intrinsic Projection of Implicit Runge-Kutta Methods for Differential-Algebraic Equations, NUMDIFF-17 Conference, Halle(Saale), Germany, September 2024.
Intrinsic Projection of Implicit Runge-Kutta Methods for Differential Algebraic Equations, SIAM Annual Meeting, Spokane, Washington, July 2024.
Intrinsic Projection of Implicit Runge-Kutta Methods for Differential Algebraic Equations, Midwest Numerical Analysis Day Conference, University of Iowa, April 2024.
Randomized FEAST, RandFEAST Working Group, Program on Numerical Analysis in Data Science, Statistical and Applied Mathematical Sciences Institute (SAMSI), October 2020.