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Section B

Numerical solution of the Sturm–Liouville problem with local RBF-based differential quadrature collocation method

Pages 285-295 | Received 05 Jan 2009, Accepted 25 Sep 2009, Published online: 26 Nov 2010
 

Abstract

In this article, we present a local RBF-based differential quadrature (LRBFDQ) collocation method for the Sturm–Liouville problem with Dirichlet, Neumann, mixed, periodic, and semi-periodic boundary conditions. Compared with the globally supported RBF (GSRBF) collocation method, this novel method approximates the derivatives by RBF interpolation using a small set of nodes in the neighbourhood of any collocation node. Less computational time is needed than the GSRBF collocation method. Compared with the GSRBF collocation method and the finite difference method (FDM), numerical results demonstrate the accuracy and easy implementation of the LRBFDQ collocation method.

2010 AMS Subject Classifications :

Acknowledgements

The author is grateful to the reviewers for their valuable comments and constructive suggestions which improved the article.

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