Unique Approaches to the Finite Difference Method

Unique Approaches to the Finite Difference Method

Presenter(s)

William Thomas Shovelton

Description

The oldest and most useful technique to approximate the solution of differential equations is the finite difference method (FDM). This technique allows for derivatives to be replaced by the finite difference discrete approximation, hence we get a finite difference equation (FDE). As with all numerical solutions, this method is only an approximation and there will be errors due to rounding and discretization. Over the years, new approaches to the FDM have been derived to improve the stability of the numerical solutions. These unique approaches are referred to as nonstandard finite difference methods (NFDM). The focus of this project will be to determine the effectiveness of two different NFDM proposed for an autonomous dynamical system and a class of reaction-diffusion equations. Effectiveness will be based on the accuracy to the exact solution and stability.

Publication Date

4-18-2018

Project Designation

Honors Thesis

Primary Advisor

Muhammad Usman

Primary Advisor's Department

Mathematics

Keywords

Stander Symposium project

Unique Approaches to the Finite Difference Method

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