A new approach for solving nonlinear singular boundary value problems

• Published in: Mathematical modelling and analysis Vol. 23; no. 1; pp. 33 - 43
• Main Authors: Zhu, Hui, Niu, Jing, Zhang, Ruimin, Lin, Yingzhen
• Format: Journal Article
• Language: English
• Published: Vilnius Vilnius Gediminas Technical University 01.01.2018
• Subjects: Boundary value problems; Convergence; Convergence (Mathematics); Kernel functions; Mathematical research; Newton methods; Nonlinear programming; nonlinear singular boundary value problem; Numerical methods; numerical solution; Quasi-Newton's method; reproducing kernel method; numerical solution; nonlinear singular boundary value problem; Quasi-Newton's method; reproducing kernel method
• ISSN: 1392-6292; 1648-3510
• DOI: 10.3846/mma.2018.003

In this paper, an e_cient method based on Quasi-Newton's method and the simpli_ed reproducing kernel method is proposed for solving nonlinear singular boundary value problems. For the Quasi-Newton's method the convergence order is studied. The uniform convergence of the numerical solution as well as its derivatives are also proved. Numerical examples are given to demonstrate the e_ciency and stability of the proposed method. The numerical results are compared with exact solutions and the outcomes of other existing numerical methods.