A six-stage third order additive method for stiff ordinary differential equations

TL;DR

This paper introduces a new third-order additive method for stiff ODEs that is L-stable, flexible in Jacobian approximation, and includes efficient automatic stepsize control, demonstrated through numerical experiments.

Contribution

It presents a novel third-order additive method for stiff ODEs that is L-stable and allows arbitrary Jacobian approximations, with integrated error and stability control.

Findings

Method is reliable and efficient in numerical experiments.

Allows arbitrary Jacobian approximation without significant computational cost.

Provides automatic stepsize selection based on local error and stability.

Abstract

In this paper we construct a third order method for solving additively split autonomous stiff systems of ordinary differential equations. The constructed additive method is L-stable with respect to the implicit part and allows to use an arbitrary approximation of the Jacobian matrix. Automatic stepsize selection based on local error and stability control are performed. The estimations for error and stability control have been obtained without significant additional computational costs. Numerical experiments show reliability and efficiency of the implemented integration algorithm.