Mesh selection strategies of the code TOM for Boundary Value Problems

Abstract

This paper presents new hybrid mesh selection strategies for boundary value problems implemented in the code TOM. Originally the code was proposed for the numerical solution of stiff or singularly perturbed problems. The code has been now improved with the introduction of three classes of mesh selection strategies, that can be used for different categories of problems. Numerical experiments show that the mesh selection and, in the nonlinear case, the strategy for solving the nonlinear equations are determinant for the good behaviour of a general purpose code. The possibility to choose the mesh selection should be considered for all general purposes codes to make them suitable for wider classes of problems.