Numerical solution of nonlinear singular boundary value problems

摘要

In this paper, an efficient method based on the simplified reproducing kernel method (SRKM) and least squares method (LSM) is proposed for solving nonlinear singular boundary value problems. The algorithm consists of two steps. First, we apply SRKM to solve a linear equation which contains a set of parameters, second the LSM is used to find the optimal parameters. Error estimation and convergence order for the presented method are also discussed. Our numerical experiments validate our theoretical findings and demonstrate the performance of the algorithm in terms of simplicity, accuracy, and efficiency.