2 NEW FINITE-DIFFERENCE SCHEMES FOR PARABOLIC EQUATIONS

Two new classes of finite difference schemes are applied to the numerical solution of parabolic partial differential equations. The formulas derived are self starting, are at least second order in time, are unconditionally stable and, unlike the Crank-Nicolson method, are L//0-stable in the sense of Gourlay and Morris. The stability of the new schemes is examined using a linear stability analysis and some numerical results are presented.