An efficient approach for solving stiff nonlinear boundary value problems

TL;DR

This paper introduces a new numerical method for efficiently solving stiff nonlinear boundary value problems, demonstrating improved stability and robustness compared to existing approaches, with validation on Troesch's problem.

Contribution

The paper presents a novel approach based on alternate approximation of the unknown function or its inverse, enhancing numerical stability for stiff problems.

Findings

Method shows increased stability on Troesch's problem

Implementation available in C++ at provided repository

Outperforms traditional methods in handling stiffness

Abstract

A new method for solving stiff boundary value problems is described and compared to other known approaches using the Troesch's problem as a test example. The method is based on the general idea of alternate approximation of either the unknown function or its inverse and has a genuine "immunity" towards numerical difficulties invoked by the rapid variation (stiffness) of the unknown solution. A c++ implementation of the proposed method is available at https://github.com/imathsoft/MathSoftDevelopment .