FOURTH-ORDER APPROXIMATION FOR NEUMANN BOUNDARY CONDITION OF HEAT CONDUCTION

摘要

A three-level compact difference scheme is proposed for the heat conduction equation with Neumann boundary conditions. By using the discrete energy method, it shows that the new method is uniquely solvable, unconditionally stable and uniformly convergent with the fully accuracy of second-order in time and fourth-order in space. A numerical example is presented to support the theoretical results.