scholarly journals A reproducing kernel method for solving nonlocal fractional boundary value problems

2012 ◽  
Vol 25 (5) ◽  
pp. 818-823 ◽  
Author(s):  
Fazhan Geng ◽  
Minggen Cui
Keyword(s):  
Boundary Value Problems ◽  
Reproducing Kernel ◽  
Kernel Method ◽  
Boundary Value ◽  
Reproducing Kernel Method ◽  
Fractional Boundary Value Problems

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.

scholarly journals CONVERGENCE ORDER OF THE REPRODUCING KERNEL METHOD FOR SOLVING BOUNDARY VALUE PROBLEMS

2016 ◽  
Vol 21 (4) ◽  
pp. 466-477 ◽  
Author(s):  
Zhihong Zhao ◽  
Yingzhen Lin ◽  
Jing Niu
Keyword(s):  
Convergence Rate ◽  
Boundary Value Problems ◽  
Reproducing Kernel ◽  
Kernel Method ◽  
Piecewise Linear ◽  
Boundary Value ◽  
Adjoint Operator ◽  
Reproducing Kernel Method ◽  
Rate Analysis ◽  
Reproducing Kernel Spaces

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.

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