TY - JOUR
T1 - On the $L_\infty$ Convergence and the Extrapolation Method of a Difference Scheme for Nonlocal Parabolic Equation with Natural Boundary Conditions
AU - Wan , Zheng-Su
AU -  , Zhi-Zhong Sun
JO - Journal of Computational Mathematics
VL - 5
SP - 449
EP - 458
PY - 2001
DA - 2001/10
SN - 19
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/8997.html
KW - Parabolic, Nonlocal, $L_\infty$ convergence, Extrapolation method.
AB - <p style="text-align: justify;">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 $L_\infty$ norm and then obtain fourth order accuracy approximation in $L_\infty$ norm by extrapolation method. At last, one numerical example is presented.</p>