Adaptive Time-Step Semi-Implicit One-Step Taylor Scheme for Stiff Ordinary Differential Equations

TL;DR

This paper introduces high-order semi-implicit Taylor-based schemes for efficiently solving stiff and non-stiff ordinary differential equations, emphasizing stability and accuracy in a unified approach.

Contribution

It presents a novel high-order semi-implicit Taylor scheme that unifies handling of stiff and non-stiff ODE components, with analysis of stability and consistency.

Findings

Schemes demonstrate improved stability for stiff ODEs

High-order accuracy achieved in numerical experiments

Unified approach simplifies solving mixed ODE problems

Abstract

In this study, we propose high-order implicit and semi-implicit schemes for solving ordinary differential equations (ODEs) based on Taylor series expansion. These methods are designed to handle stiff and non-stiff components within a unified framework, ensuring stability and accuracy. The schemes are derived and analyzed for their consistency and stability properties, showcasing their effectiveness in practical computational scenarios.