ON THE L_∞ CONVERGENCE AND THE EXTRAPOLATION METHOD OF A DIFFERENCE SCHEME FOR NONLOCAL PARABOLIC EQUATION WITH NATURAL BOUNDARY

摘要

In paper [4] 9J. Comput. Appl. Math. 76 (1996), 137-146), a difference scheme for a class of nonlocal parabolic equations with natural boundary conditions was derived by the method of reduction of order and the unique solvability and second order convergence in L_2-norm are proved. In this paper, we prove that the scheme is second order conver- gent in L_∞ norm and then obtain fourth order accuracy approximation in L_∞ norm by extrapolation method. At last, one numerical example is presented.