ScholarLens Back to search
1988•SIAM Journal on Numerical AnalysisRequires access

Error Estimates and Adaptive Time-Step Control for a Class of One-Step Methods for Stiff Ordinary Differential Equations

Claes Johnson

Open publisher page 146 citations

Abstract

We prove new optimal a priori error estimates for a class of implicit one-step methods for stiff ordinary differential equations obtained by using the discontinuous Galerkin method with piecewise polynomials of degree zero and one. Starting from these estimates we propose a new algorithm for automatic time-step control and we discuss the relation between this algorithm and earlier algorithms implemented in packages for the numerical solution of stiff ordinary differential equations.

About this research paper

What this paper is about

We prove new optimal a priori error estimates for a class of implicit one-step methods for stiff ordinary differential equations obtained by using the discontinuous Galerkin method with piecewise polynomials of degree zero and one. Starting from these estimates we propose a new algorithm for automatic time-step control and we discuss the relation between this algorithm and earlier algorithms implemented in packages for the numerical solution of stiff ordinary differential equations.

Why it matters

OpenAlex reports 146 citations for this work. Citation counts describe recorded attention and do not establish research quality.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

We prove new optimal a priori error estimates for a class of implicit one-step methods for stiff ordinary differential equations obtained by using the discontinuous Galerkin method with piecewise polynomials of degree zero and one. Starting from these estimates we propose a new algorithm for automatic time-step control and we discuss the relation between this algorithm and earlier algorithms implemented in packages for the numerical solution of stiff ordinary differential equations.

Key concepts: Mathematics, Piecewise, Ordinary differential equation, A priori and a posteriori, Galerkin method, Applied mathematics, Explicit and implicit methods, Backward differentiation formula

Related papers

Related paper 1Related paper 2Related paper 3
Back to paper searchBrowse research topicsOriginal source
Error Estimates and Adaptive Time-Step Control for a Class of One-Step Methods for Stiff Ordinary Differential Equations — Research Paper | ScholarLens