Numerical method for a class of singular non-linear boundary value problems using Green's functions

摘要

A numerical method based on Green's function is presented for solving a class of singular non-linear boundary value problems. By applying Green's function an equivalent integral equation, which can be solved by linear interpolation on a non-uniform mesh, can be derived from the singular non-linear boundary value problem. This equation is shown to be second-order convergent. The numerical method can be extended to more general singular boundary value problems. Numerical experiments support these theoretical results and indicate that the estimates are sharp.