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A frequency accurate r th order spatial derivative finite difference approximation
Author(s) -
Orlin Peter A.,
Perkins A. Louise
Publication year - 1999
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/(sici)1098-2426(199909)15:5<569::aid-num4>3.0.co;2-3
Subject(s) - mathematics , partial derivative , finite difference , a priori and a posteriori , partial differential equation , nonlinear system , derivative (finance) , finite difference method , mathematical analysis , polynomial , dissipation , differential (mechanical device) , philosophy , physics , epistemology , quantum mechanics , financial economics , economics , thermodynamics , engineering , aerospace engineering
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. © 1999 John Wiley & Sons, Inc. * Numer Methods Partial Differential Eq 15: 569–580, 1999