Runge-Kutta Lawson schemes for stochastic differential equations

TL;DR

This paper introduces a new class of stochastic Runge-Kutta Lawson schemes that maintain the convergence of traditional methods while offering enhanced stability for solving stochastic differential equations.

Contribution

The paper develops a general framework for stochastic Runge-Kutta Lawson schemes, demonstrating their inheritance of convergence and improved stability over existing methods.

Findings

Schemes inherit convergence properties of underlying Runge-Kutta methods.

Numerical experiments confirm the schemes' effectiveness.

New schemes show improved stability in examples.

Abstract

In this paper, we present a framework to construct general stochastic Runge-Kutta Lawson schemes. We prove that the schemes inherit the consistency and convergence properties of the underlying Runge-Kutta scheme, and confirm this in some numerical experiments. We also investigate the stability properties of the methods and show for some examples, that the new schemes have improved stability properties compared to the underlying schemes.