Convergence Order of the Reproducing Kernel Method for Solving Boundary Value Problems

• Published in: Mathematical modelling and analysis Vol. 21; no. 4; pp. 466 - 477
• Main Authors: Zhao, Zhihong, Lin, Yingzhen, Niu, Jing
• Format: Journal Article
• Language: English
• Published: Taylor & Francis 03.07.2016; Vilnius Gediminas Technical University
• Subjects: Adjoints; boundary value problem; Boundary value problems; Convergence; Convergence (Mathematics); convergence analysis; Equivalence; Kernel functions; Kernels; Mathematical analysis; Mathematical models; Mathematical research; Operators (mathematics); reproducing kernel method; convergence analysis; boundary value problem; reproducing kernel method
• ISSN: 1392-6292; 1648-3510
• DOI: 10.3846/13926292.2016.1183240

In this paper, convergence rate of the reproducing kernel method for solving boundary value problems is studied. The equivalence of two reproducing kernel spaces and some results of adjoint operator are proved. Based on the classical properties of piecewise linear interpolating function, we provide the convergence rate analysis of at least second order. Moreover, some numerical examples showing the accuracy of the proposed estimations are also given.