A FINITE-DIFFERENCE SCHEME FOR PARTIAL INTEGRODIFFERENTIAL EQUATIONS WITH A WEAKLY SINGULAR KERNEL

A finite difference method for the numerical solution of partial integro-differential equations is considered. In the time direction, a Crank-Nicolson time-stepping is used to approximate the differential term and the product trapezoidal method is employed to treat the integral term. An error bound is derived for the numerical scheme. Due to lack of smoothness of the exact solution, the overall numerical procedure does not achieve second-order convergence in time. But the convergence order in time is shown to be greater than one, which is confirmed by a numerical example.