Singular boundary value problems for ODEs

摘要

This paper is concerned with the numerical solution of a system of ordinary differential equations (ODEs), y′=Sy/t+f(t,y,p), on an interval [0,b] subject to boundary conditions 0=g(y(0),y(b),p). The ODEs have a coefficient that is singular at t=0, but it is assumed that the boundary value problem (BVP) has a smooth solution. Some popular methods for BVPs evaluate the ODEs at t=0. This paper deals with the practical issues of solving this class of singular BVPs with such a method. The bvp4c solver of Matlab has been modified accordingly so that it can solve a class of singular BVPs as effectively as it previously solved non-singular BVPs.