Application of Operator Splitting to Solve Reaction Diffusion Equations

TL;DR

This paper investigates various operator splitting methods for solving the Fisher reaction-diffusion equation, analyzing their errors and orders both numerically and symbolically to improve solution accuracy.

Contribution

It introduces a comprehensive analysis of splitting methods applied to nonlinear reaction-diffusion equations, including error and order calculations.

Findings

Different splitting methods have varying errors and orders.

Numerical and symbolic calculations provide insights into method performance.

The study enhances understanding of operator splitting effectiveness for nonlinear PDEs.

Abstract

Approximate solutions of the Fisher equation obtained by different splitting methods are investigated. The error of this nonlinear problem is analyzed. The order of different splitting methods coupled with numerical methods of different order is calculated numerically and symbolically.