A Compact Scheme For A Partial Integro-Differential Equation With Weakly Singular Kernel

Compact finite difference scheme is applied for a partial integro-differential equation with a weakly singular kernel. the product trapezoidal method is applied for discretization of the integral term. the order of accuracy in space and time is o(h4,k2-a ),where 0 <α<1. stability and convergence in 2 l norm are discussed through energy method. numerical examples are provided to confirm the theoretical prediction and to show that the combination of the compact finite difference approximation and product trapezoidal method give an efficient method for solving a partial integro-differential equation.