Performance of Borel-Pad\'e-Laplace integrator for the resolution of stiff and non-stiff problems

TL;DR

This paper evaluates the Borel-Padé-Laplace integrator's stability and efficiency in solving stiff and non-stiff differential equations, comparing its performance with other established numerical schemes.

Contribution

It provides a stability analysis and numerical performance assessment of the Borel-Padé-Laplace integrator for various differential equations, highlighting its advantages and limitations.

Findings

The integrator is stable for certain stiff problems.

It performs comparably or better than popular schemes.

Effective for both ordinary and partial differential equations.

Abstract

A stability analysis of the Borel-Laplace series summation technique, used as explicit time integrator, is carried out. Its numerical performance on stiff and non-stiff problems is analyzed. Applications to ordinary and partial differential equations are presented. The results are compared with those of many popular schemes designed for stiff and non-stiff equations.