A-CONVERGENCE OF FINITE-DIFFERENCE APPROXIMATIONS OF PARABOLIC INITIAL-BOUNDARY VALUE-PROBLEMS

The Crank-Nicolson method and a further method, called the Richtmyer-Morton method, are applied to one-dimensional parabolic initial-boundary value problems involving a strongly elliptic operator L. It is shown for time-independent linear L that these methods are A-convergent and accurate. In the case of time-dependent weakly nonlinear L, relative to the discrete L//2-norm, results are derived for both methods.