An efficient computational method for a class of singularly perturbed delay parabolic partial differential equation

Abstract

In this paper, a new technique is constructed skillfully in order to solve a class of singularly perturbed delay parabolic partial differential equation. The outer and inner exact solutions of the linear problem can be expressed in the form of series and the outer and inner approximate solutions of the nonlinear problem are given by the iterative formula. Compared with known investigations, the advantages of our method are that the representation of the exact solution is obtained by using a new technique in a new reproducing kernel Hilbert space and the accuracy of numerical computation is higher. Two numerical examples are studied to demonstrate the accuracy of the present method. Results obtained by the method indicate that it is simple and effective.

Keywords:

• singular perturbation
• reproducing kernel
• delay partial differential equations

2000 AMS Subject Classifications :

• 41A30
• 35K50
• 35D05
• 39A14

Acknowledgements

The authors thank the reviewers for their valuable suggestions, which greatly improved the quality of the paper. This study is supported by the Natural Science Foundation of Inner Mongolia (No. 2009MS0103), the college science research project of Inner Mongolia (No. NJZY08057) and the project of Inner Mongolia University of Technology (No. ZS201036).