Application of reproducing kernel method to third order three-point boundary value problems

2010 ◽  
Vol 217 (7) ◽  
pp. 3425-3428 ◽  
Author(s):  
Boying Wu ◽  
Xiuying Li
Keyword(s):  
Boundary Value Problems ◽  
Reproducing Kernel ◽  
Kernel Method ◽  
Boundary Value ◽  
Point Boundary ◽  
Third Order ◽  
Reproducing Kernel Method

scholarly journals Fitted Reproducing Kernel Method for Solving a Class of Third-Order Periodic Boundary Value Problems

2016 ◽  
Vol 13 (5) ◽  
pp. 501-510 ◽  
Author(s):  
Asad Freihat ◽  
Radwan Abu-Gdairi ◽  
Hammad Khalil ◽  
Eman Abuteen ◽  
Mohammed Al-Smadi ◽  
...  
Keyword(s):  
Boundary Value Problems ◽  
Periodic Boundary ◽  
Reproducing Kernel ◽  
Kernel Method ◽  
Boundary Value ◽  
Third Order ◽  
Reproducing Kernel Method ◽  
Periodic Boundary Value Problems

scholarly journals The Solution of a Class of Third-Order Boundary Value Problems by the Reproducing Kernel Method

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Zhiyuan Li ◽  
Yulan Wang ◽  
Fugui Tan
Keyword(s):  
Analytical Solution ◽  
Boundary Value Problems ◽  
Reproducing Kernel ◽  
Kernel Method ◽  
Boundary Value ◽  
Nonlinear Boundary Conditions ◽  
Reproducing Kernel Space ◽  
Third Order ◽  
Reproducing Kernel Method ◽  
Computation Efficiency

This paper expands the application of reproducing kernel method to a class of third-order boundary value problems with mixed nonlinear boundary conditions. The analytical solution is represented in the form of series in the reproducing kernel space. Then-term approximation is obtained and is proved to converge to the analytical solution. The numerical examples are given to demonstrate the computation efficiency of the presented method. Results obtained by the method indicate that the method is simple and effective.

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.

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