Solutions of Second Order Three Point BVP Using Combination of Adomian Decomposition Method and Reproducing Kernel Method

2015 ◽  
Vol 4 (1) ◽  
pp. 73-76
Author(s):  
Hamood ur Rehman ◽  
Muhammad Usman Malik ◽  
Muzammal Iftikhar ◽  
Muhammad Younis ◽  
M. Shoaib Saleem
Keyword(s):  
Decomposition Method ◽  
Reproducing Kernel ◽  
Kernel Method ◽  
Adomian Decomposition Method ◽  
Second Order ◽  
Reproducing Kernel Method ◽  
Adomian Decomposition

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.

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