The solution of a class of third-order boundary value problems by the reproducing kernel method
type: Item
instance of: scholarly article
title: The solution of a class of third-order boundary value problems by the reproducing kernel method
zbMATH Open document ID: 1258.34035
DOI: 10.1155/2012/195310
author: Fugui Tan
author: Zhiyuan Li
author: Yulan Wang
published in: Abstract and Applied Analysis
publication date: 2012-12-18T00:00:00Z
review text: Summary: This paper expands the application of the 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. The \(n\)-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.
Mathematics Subject Classification ID: 34A45
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 65L10
zbMATH DE Number: 6116341
Wikidata QID: Q58695933
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/195310
OpenAlex ID: W2142430236
cites work: B-spline collocation for solution of two-point boundary value problems
cites work: The numerical solution of third-order boundary-value problems with fourth-degree &B-spline functions
cites work: The numerical solution of third-order boundary-value problems using quintic splines
cites work: A numerical method for third-order non-linear boundary-value problems in engineering
cites work: The use of Adomian decomposition method for solving problems in calculus of variations
cites work: Method of weighted residuals as applied to higher order, nonlinear, two-point boundary value problems
cites work: Using reproducing kernel for solving a class of partial differential equation with variable-coefficients
cites work: A new method for solving a class of mixed boundary value problems with singular coefficient
cites work: The exact solution of system of linear operator equations in reproducing kernel spaces
cites work: New algorithm for second-order boundary value problems of integro-differential equation
cites work: Nonpolynomial spline approach to the solution of a system of third-order boundary-value problems
cites work: Quartic splines solutions of third-order obstacle problems
cites work: Numerical solutions for system of third-order boundary value problems
cites work: Cubic splines method for a system of third-order boundary value problems
cites work: A numerical approach for odd-order obstacle problems
cites work: Finite difference scheme for variational inequalities
cites work: Solving third-order obstacle problems with quartic \(B\)-splines
description: scientific article; zbMATH DE number 6116341