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A new fourth‐order numerical algorithm for a class of three‐dimensional nonlinear evolution equations
Author(s) -
Deng Dingwen,
Zhang Chengjian
Publication year - 2013
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.21701
Subject(s) - mathematics , extrapolation , richardson extrapolation , nonlinear system , norm (philosophy) , dimension (graph theory) , partial differential equation , class (philosophy) , partial derivative , stability (learning theory) , algorithm , mathematical analysis , computer science , pure mathematics , quantum mechanics , artificial intelligence , machine learning , political science , law , physics
Abstract In this article, a new compact alternating direction implicit finite difference scheme is derived for solving a class of 3‐D nonlinear evolution equations. By the discrete energy method, it is shown that the new difference scheme has good stability and can attain second‐order accuracy in time and fourth‐order accuracy in space with respect to the discrete H 1 ‐norm. A Richardson extrapolation algorithm is applied to achieve fourth‐order accuracy in temporal dimension. Numerical experiments illustrate the accuracy and efficiency of the extrapolation algorithm. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013