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A compact locally one‐dimensional finite difference method for nonhomogeneous parabolic differential equations
Author(s) -
Qin Jinggang,
Wang Tongke
Publication year - 2011
Publication title -
international journal for numerical methods in biomedical engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.741
H-Index - 63
eISSN - 2040-7947
pISSN - 2040-7939
DOI - 10.1002/cnm.1299
Subject(s) - compact finite difference , mathematics , parabolic partial differential equation , computation , norm (philosophy) , finite difference method , mathematical analysis , ftcs scheme , partial differential equation , order of accuracy , finite difference , differential equation , numerical partial differential equations , algorithm , ordinary differential equation , differential algebraic equation , political science , law
Abstract This paper is concerned with accurate and efficient numerical methods for solving parabolic differential equations. A compact locally one‐dimensional finite difference method is presented, which has second‐order accuracy in time and fourth‐order accuracy in space with respect to discrete H 1 norm and L 2 norm. The scheme is proved to be unconditionally stable. All computations are implemented in one direction and the CPU time is relatively smaller compared with some other compact computational schemes. Numerical results are presented to show the accuracy and efficiency of the new algorithm for the parabolic differential equations. Copyright © 2009 John Wiley & Sons, Ltd.