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.