New collocation approaches based on reproducing kernel functions for second order nonlinear boundary value problems

Abstract

In the previous work, the reproducing kernel Hilbert space (RKHS) theory has been employed mainly to solve linear boundary value problems (BVPs). Reproducing kernel functions (RKFs) based techniques for nonlinear BVPs mainly applied iterative techniques. However, there is no error analysis for these methods. In this letter, we shall propose new collocation algorithms based on RKFs for dealing with second order nonlinear BVPs. And the detailed error analysis is provided.