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Section B

Quasi-wavelet based numerical method for fourth-order partial integro-differential equations with a weakly singular kernel

, &
Pages 3236-3254 | Received 04 Jul 2010, Accepted 02 May 2011, Published online: 14 Jul 2011
 

Abstract

In this paper, we study the numerical solution of initial boundary-value problem for the fourth-order partial integro-differential equations with a weakly singular kernel. We use the forward Euler scheme for time discretization and the quasi-wavelet based numerical method for space discretization. Detailed discrete formulations are given to the treatment of three different boundary conditions, including clamped-type condition, simply supported-type condition and a transversely supported-type condition. Some numerical experiments are included to demonstrate the validity and applicability of the discrete technique. The comparisons of present results with analytical solutions show that the quasi-wavelet based numerical method has a distinctive local property. Especially, the method is easy to implement and produce very accurate results.

2011 AMS Subject Classifications :

Acknowledgements

This work was supported by the National Nature Science Foundation of China (No. 10271046, 10971062). The authors thank the anonymous reviewers for their invaluable comments and suggestions.

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