A High-Order Numerical Method for a Nonlinear System of Second-Order Boundary Value Problems. (9th March 2020)

• Record Type: Journal Article
• Authors: Xu, Minqiang; Niu, Jing; Guo, Li
• Other Names: Schuster Thomas Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2020(2020)
• Publication Date: 2020-03-09
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2020/6280372
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : 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.