Stochastic numerical treatment for solving Troesch’s problem

Abstract

In this article, the numerical techniques are presented for the solution of Troesch’s problem based on neural networks optimized with three different methods including particle swarm optimization (PSO), active set (AS) and PSO hybridized with AS (PSO-AS) algorithms. The variable transformation is applied in order to convert the original problem to a transformed problem which is relatively less stiff to solve. Feed-forward artificial neural networks are used to model the transformed problem. Learning of adjustable parameters is made with PSO, AS and PSO-AS algorithms. The proposed methodologies are applied to a number of cases for stiff and non-stiff boundary value problems. The comparative analyses are carried out with other standard numerical solutions, as well as approximate analytical solver.