Mathematics Faculty Proceedings, Presentations, Speeches, Lectures
A splitting approximation for the numerical solution of a self-adjoint quenching problem
Event Name/Location
Joint Mathematics Meetings, Colorado Convention Center
Date Range
January 15-18, 2020
Presentation Date
1-2020
Document Type
Conference Presentation
ORCID ID
0000-0001-7817-4308
Description
Ideal combustion processes are often modelled via nonlinear reaction-diffusion equations with singular forcing terms. Our preliminary work considers the numerical solution of such a partial differential equation problem, where a self-adjoint operator with variable diffusion coefficient is considered. Traditional Peaceman-Rachford-Strang splitting is used for time stepping of the semi-discrete system of equations obtained. Conditions are derived to ensure the monotonicity, positivity, and linear stability of the finite difference method. Simulation experiments are provided to validate our splitting approximation.
NSUWorks Citation
Kabre, Julienne, "A splitting approximation for the numerical solution of a self-adjoint quenching problem" (2020). Mathematics Faculty Proceedings, Presentations, Speeches, Lectures. 433.
https://nsuworks.nova.edu/cnso_math_facpres/433
Comments
Part of the AMS Special Session on Highly Accurate and Structure-Preserving Numerical Methods for Nonlinear Partial Differential Equations, I