The multistep finite difference fractional steps method for a class of viscous wave equations

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 l2 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.

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