Corrigendum to “On the solutions of a second order nonlinear system with almost periodic forcing” [Commun Nonlinear Sci Numer Simulat 15 (2010) 3525–3535]

2011 ◽  
Vol 16 (3) ◽  
pp. 1702
Author(s):  
Muren Lin ◽  
Yong-Hui Xia
Keyword(s):  
Nonlinear System ◽  
Second Order ◽  
Almost Periodic ◽  
Periodic Forcing

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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