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

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.

Keywords:

• integro-differential equation
• weakly singular
• quasi-wavelets
• the forward Euler scheme

2011 AMS Subject Classifications :

• 35R09
• 45K05
• 65M99
• 65T60

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.