On solving parabolic equation with homogeneous boundary and integral initial conditions

摘要

In this paper we consider the second order parabolic partial di.erential equa- tion with constant coe.cients subject to homogeneous Dirichlet boundary conditions and initial condition containing nonlo cal integral term. We derive first and second order finite di.erence schemes for the parabolic problem, combining implicit and Crank-Nicolson metho ds with two discretizations of the integral term. One numerical example is presented to test and illustrate the proposed algorithm.