Characterizing and minimizing the operator split error for Fisher’s equation

Abstract

Operator splitting (OS) is a popular and convenient technique used to numerically solve reactive transport problems such as Fisher’s equation. Although OS has been widely used to solve Fisher’s equation, no characterization of the innate OS error has been presented. Here the exact characteristics of the OS error for travelling wave solutions of Fisher’s equation are revealed and explored. The analysis shows that the OS error behaves differently to previously studied linear problems by smoothing or steepening the wave front depending on the sequential order of splitting. Further analysis confirms that the OS error is reduced by implementing an alternating OS scheme.