Automated allocation of mesh points for stiff two-point boundary value problems

Abstract

The numerical solution of a stiff two-point boundary value problem is considered where a general procedure to automate the allocation of mesh points is obtained. This procedure requires negligible prerequisites to the problem. The automation is achieved by constructing a diffeomorphism ψ acting on the domain of the independent variable. This ψ smooths out the sharp corners in the solution while it leaves the domain boundary and the boundary conditions unchanged. The diffeomorphism is defined by differential equations which are coupled with the original equations to form an augmented system.