A Legendre reproducing kernel method with higher convergence order for a class of singular two-point boundary value problems

2021 ◽  
Author(s):  
Minqiang Xu ◽  
Emran Tohidi
Keyword(s):  
Boundary Value Problems ◽  
Reproducing Kernel ◽  
Kernel Method ◽  
Boundary Value ◽  
Convergence Order ◽  
Point Boundary ◽  
Reproducing Kernel Method

scholarly journals A High-Order Numerical Method for a Nonlinear System of Second-Order Boundary Value Problems

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Minqiang Xu ◽  
Jing Niu ◽  
Li Guo
Keyword(s):  
Nonlinear System ◽  
Boundary Value Problems ◽  
Numerical Experiments ◽  
Reproducing Kernel ◽  
Kernel Method ◽  
Boundary Value ◽  
Linear Equations ◽  
Second Order ◽  
High Order ◽  
Reproducing Kernel Method

This paper is concerned with a high-order numerical scheme for nonlinear systems of second-order boundary value problems (BVPs). First, by utilizing quasi-Newton’s method (QNM), the nonlinear system can be transformed into linear ones. Based on the standard Lobatto orthogonal polynomials, we introduce a high-order Lobatto reproducing kernel method (LRKM) to solve these linear equations. Numerical experiments are performed to investigate the reliability and efficiency of the presented method.

Sign in / Sign up

Export Citation Format

Share Document