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The multistep finite difference fractional steps method for a class of viscous wave equations
Author(s) -
Zhang Zhiyue
Publication year - 2010
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1371
Subject(s) - mathematics , wave equation , norm (philosophy) , stability (learning theory) , finite difference coefficient , finite difference , von neumann architecture , linear multistep method , multiplicative function , finite difference method , mathematical analysis , a priori and a posteriori , finite element method , pure mathematics , differential equation , mixed finite element method , law , differential algebraic equation , ordinary differential equation , philosophy , physics , epistemology , machine learning , political science , computer science , thermodynamics
In this paper, a new multistep finite difference fractional method applicable to parallel arithmetic for viscous wave equation is proposed. Some techniques, such as calculus of variations, multiplicative commutation rule of difference operators, decomposition of high‐order difference operators and priori estimates are adopted. It is shown that the scheme is second‐order in temporal and spacial direction in the l 2 norm. The new scheme is unconditionally stable for initial value by using the Von Neumann linear stability analysis. Experiments show that the new method is very efficient for solving viscous wave equation, which is of vital importance in life sciences. Copyright © 2010 John Wiley & Sons, Ltd.