Solving a class of singular two-point boundary value problems using new effective reproducing kernel technique

Abstract

Based on reproducing kernel theory, an efficient reproducing kernel technique is proposed for solving a class of singular two-point boundary value problems with Dirichlet boundary conditions. It is implemented as a new reproducing kernel method. In this method, reproducing kernels with Chebyshev polynomials form are used. Convergence analysis and an error estimation for the method in Lw2 space are discussed. The numerical solutions obtained by the method are compared with the numerical results of reproducing kernel method (RKM). The results reveal that the proposed method is quite efficient and accurate.