Degree

Doctor of Philosophy (PhD)

Department

Mathematics

Document Type

Dissertation

Abstract

Reaction-diffusion systems, as examples of semilinear parabolic partial differential equations, have played significant roles in the mathematical modeling of physical, chemical, and biological processes. Several reaction-diffusion systems typically do not have exact solutions in closed form, and numerically solving them also comes with challenges due to the presence of the nonlinear local interaction/chemical reaction dynamics representing the reaction term, coupling between components, multidimensionality of the diffusion operator, and stiffness of the diffusion and/or reaction terms. Wederive and analyze several second-order accurate exponential integrators of the Strang type for the time discretization of stiff reaction-diffusion systems. We utilize the finite difference technique for spatial discretization. The dimensional splitting of the spatial discretization matrix, Strong Stability Preserving Runge-Kutta (SSP-RK2), Integrating Factor (IF), and Strang operator splitting methods are employed in the development of L-stable and easily parallelizable numerical algorithms presented in this dissertation, where all the matrix exponentials involved are evaluated with the rational approximant (non-Padé type) having distinct and real poles. We also present a rigorous error and stability analysis of a proposed scheme. Numerical results validate that the proposed numerical methods are superior in efficiency, expected order of convergence, and accuracy compared to several existing competitive second-order accurate numerical schemes such as ETD-Padé, IMEX, and ETD-RDP schemes.

Date

2-6-2026

DOI

https://proquest.com/docview/3347819056

First Committee Chair

Bruce Wade

First Committee Member

Olaniyi Iyiola

Second Committee Member

Xiang-Sheng Wang

Third Committee Member

Yangwen Zhang

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