Mathematics Faculty Proceedings, Presentations, Speeches, Lectures

Title

A splitting approximation for the numerical solution of a self-adjoint quenching problem

Event Name/Location

Joint Mathematics Meetings, Colorado Convention Center

Event Name

Joint Mathematics Meetings

Event Location

Colorado Convention Center

Document Type

Conference Presentation

Publication Date

1-2020

Date Range

January 15-18, 2020

Abstract

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.

Comments

Part of the AMS Special Session on Highly Accurate and Structure-Preserving Numerical Methods for Nonlinear Partial Differential Equations, I

ORCID ID

0000-0001-7817-4308

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