The norm convergence of a Magnus expansion method

TL;DR

This paper investigates the convergence order of a basic Magnus expansion method for numerically solving non-autonomous evolution equations, providing insights into its accuracy and potential applications.

Contribution

It analyzes the convergence order of the simplest Magnus method, offering new theoretical understanding of its performance.

Findings

Establishes the convergence order of the Magnus method

Provides theoretical bounds for approximation accuracy

Enhances understanding of numerical solutions for evolution equations

Abstract

We consider numerical approximation to the solution of non-autonomous evolution equations. The order of convergence of the simplest possible Magnus method will be investigated.