An explicit two-step method for solving stiff systems of ordinary differential equations

Abstract

In this paper we propose a numerical method to integrate stiff ordinary differential systems of the form Y′ = f(t Y)t ∊ [t ₀ t _N ]Y ∊ R ^m m positive integer, with Y(t ₀) = Y ₀.

The method is an explicit two-step scheme, with variable coefficients, depending on a stability parameter. We prove that the scheme is of the first order in accuracy and that it shows good stability properties. We conclude by giving some numerical results obtained solving known stiff systems of differential equations.

Keywords:

• Multi-step methods
• stiff systems
• A-stability

C.R. Categories:

• G.1.7

Work performed under the auspices of the “Centro Interuniversitario di Analisi Numerica e Matematica Computazionale”.

Work performed under the auspices of the “Centro Interuniversitario di Analisi Numerica e Matematica Computazionale”.

Notes

Work performed under the auspices of the “Centro Interuniversitario di Analisi Numerica e Matematica Computazionale”.