A frequency accurate r(th) order spatial derivative finite difference approximation
A method for the specification and design of finite difference spatial derivative approximations of general order r is presented. The method uses a difference polynomial with undetermined coefficients. Spatial frequency domain-based criteria, which include phase velocity, group velocity, and dissipation requirements at a priori selected spatial frequencies, are used to find the appropriate coefficient values. The method is formulated as an optimal design problem but is pursued heuristically. The general derivative approximation and the design method are suitable for use in more general design problems involving finite difference schemes for linear and nonlinear partial differential equations. (C) 1999 John Wiley & Sons, Inc.
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
(1999). A frequency accurate r(th) order spatial derivative finite difference approximation. NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 15(5), 569-580.
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