Two-step General Linear Methods for Retarded Functional Differential Equations

TL;DR

This paper introduces a new class of two-step general linear methods designed specifically for efficiently solving retarded functional differential equations, including explicit methods up to order five, with strategies to mitigate order reduction in stiff problems.

Contribution

The paper develops a novel class of two-step general linear methods tailored for retarded functional differential equations, achieving high order accuracy and improved stability properties.

Findings

Explicit methods up to order five constructed.

Methods designed to avoid order reduction in mildly stiff problems.

Uniform stage order close to uniform order enhances stability.

Abstract

This paper presents a class of Two-Step General Linear Methods for the numerical solution of Retarded Functional Differential Equations. Explicit methods up to order five are constructed. To avoid order reduction for mildly stiff problems the uniform stage order of the methods is chosen to be close to uniform order.