Abstract

In this paper we consider the second order parabolic partial differential equation with constant coefficients subject to homogeneous Dirichlet boundary conditions and initial condition containing nonlocal integral term. We derive first and second order finite difference schemes for the parabolic problem, combining implicit and Crank-Nicolson methods with two discretizations of the integral term. One numerical example is presented to test and illustrate the proposed algorithm.

Keywords: Finite difference method; stability estimate; parabolic equation; non-local condition; second-order of convergence.

MSC: 65M12, 65M06, 65M22

Pages:  258$-$268     

Volume  67 ,  Issue  4 ,  2015