A transformation-based approach for solving stiff two-point boundary value problems

TL;DR

This paper introduces a transformation-based framework that enhances the stiffness resistance of numerical methods for solving two-point boundary value problems, demonstrated with the trapezoidal scheme and supported by numerical experiments.

Contribution

It generalizes and extends existing methods to improve stiffness handling in boundary value problem solvers, applicable to various numerical schemes.

Findings

Enhanced stiffness resistance demonstrated with the trapezoidal scheme

The approach is adaptable to multiple numerical methods

Numerical experiments support theoretical claims

Abstract

A new approach for solving stiff boundary value problems for systems of ordinary differential equations is presented. Its idea essentially generalizes and extends that from arXiv:1601.04272v8. The approach can be viewed as a methodology framework that allows to enhance "stiffness resistance" capabilities of pretty much all the known numerical methods for solving two-point BVPs. The latter is demonstrated on the example of the {\it trapezoidal scheme} with the corresponding C++ source code available at \url{https://github.com/imathsoft/MathSoftDevelopment}. Results of numerical experiments are provided to support the theoretical conclusions.