Semianalytic numerical studies of turning points arising in stiff boundary value problems

Abstract

A numerical algorithm for solving stiff boundary value problems with turning points is presented. The stiff systems are characterized as singularly perturbed differential equations. The numerical method is derived by appropriately discretizing the boundary layer and connection theory for such systems. Numerical results demonstrate the effectiveness of the method. In many cases the calculation proceeds with mesh increments which are orders of magnitude larger than those used by other known methods.