Efficient solution of a class of partial integro-differential equation in reproducing kernel space

Abstract

In [Y.l. Wang, T. Chaolu, Z. Chen, Using reproducing kernel for solving a class of singular weakly nonlinear boundary value problems, Int. J. Comput. Math. 87(2) (2010), pp. 367–380], we present three algorithms to solve a class of ordinary differential equations boundary value problems in reproducing kernel space. It is worth noting that our methods can get the solution of partial integro-differential equation. In this note, we use method 2 [M. Dehghan, Solution of a partial integro-differential equation arising from viscoelasticity, Int. J. Comput. Math. 83(1) (2006), pp. 123–129] to solve a class of partial integro-differential equation in reproducing kernel space. Numerical example shows our method is effective and has high accuracy.

Keywords:

• partial integro-differential equation
• reproducing kernel
• reproducing kernel space

2000 AMS Subject Classifications :

• 45K05
• 34K28
• 47G20

Acknowledgements

The authors thank the reviewers for their valuable suggestions, which greatly improved the quality of the paper. This paper is supported by the college science research project of Inner Mongolia (NJZY08057, NJZY07066 and 2009MS0103).