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

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  • Minqiang Xu
  • Jing Niu
  • Li Guo

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.

Suggested Citation

  • Minqiang Xu & Jing Niu & Li Guo, 2020. "A High-Order Numerical Method for a Nonlinear System of Second-Order Boundary Value Problems," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-7, March.
    • Handle: RePEc:hin:jnlmpe:6280372
    DOI: 10.1155/2020/6280372
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