Numerical Algorithm for the Third-Order Partial Differential Equation with Three-Point Boundary Value Problem

A numerical method based on the reproducing kernel theorem is presented for the numerical solution of a three-point boundary value problem with an integral condition. Using the reproducing property and the existence of orthogonal basis in a new reproducing kernel Hilbert space, we obtain a represent...

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Bibliographic Details
Published in:Abstract and Applied Analysis 2014-01, Vol.2014 (2014), p.412-418-1039
Main Authors: Niu, Jing, Lin, Yingzhen
Format: Article
Language:English
Subjects:
Algorithms
Boundary value problems
Differential equations, Partial
Finite element analysis
Mathematical models
Mathematical research
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Summary:A numerical method based on the reproducing kernel theorem is presented for the numerical solution of a three-point boundary value problem with an integral condition. Using the reproducing property and the existence of orthogonal basis in a new reproducing kernel Hilbert space, we obtain a representation of exact solution in series form and its approximate solution by truncating the series. Moreover, the uniform convergency is proved and the effectiveness of the proposed method is illustrated with some examples.
ISSN:1085-3375
1687-0409
DOI:10.1155/2014/630671