On the $L_∞$ Convergence and the Extrapolation Method of a Difference Scheme for Nonlocal Parabolic Equation with Natural Boundary Conditions (Journal of Computational Mathematics, 2001)
In paper [4] (J. 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 convergent in $L_∞$ norm and then obtain fourth order accuracy approximation in $L_∞$ norm by extrapolation method. At last, one numerical example is presented.