Date of Award
5-2025
Degree Type
Honors College Thesis
Academic Program
Mathematics BS
Department
Mathematics
First Advisor
James Lambers, Ph.D
Advisor Department
Mathematics
Abstract
This thesis introduces a novel method for solving systems of Ordinary Differential Equations (ODEs) resulting from the spatial discretization of Partial Differential Equations (PDEs). The proposed approach builds upon an existing technique that employs Krylov projection, which requires evaluating a matrix function at each timestep. The innovation of the new method lies in its reuse strategy, which shifts the perspective from direct matrix function evaluation to polynomial interpolation. Numerical experiments conducted on constant and variable coefficient heat equations, with both smooth and discontinuous initial data, demonstrate the computational time advantage of the new approach. The results indicate that this method is promising and warrants further investigation.
Copyright
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Recommended Citation
Vasilyeva, Anzhelika, "Globally Adaptive Exponential Integrators for Stiff Systems of ODEs" (2025). Honors Theses. 1042.
https://aquila.usm.edu/honors_theses/1042
Comments
Honors College Award: Excellence in Research