Compact finite difference schemes of sixth order for the Helmholtz equation

Journal of Computational and Applied Mathematics

Volumn 203, Issue 1, 2007, Pages 15-31

  Sutmann, Godehard ^a  

^a FORSCHUNGSZENTRUM JÜLICH   (Germany)

Author keywords

Combination of finite difference schemes; Helmholtz equation; High order compact solvers; Pad approximation

Indexed keywords

APPROXIMATION THEORY; COMPUTATIONAL METHODS; ERROR ANALYSIS; NONLINEAR EQUATIONS; PROBLEM SOLVING;

FINITE DIFFERENCE SCHEMES; HELMHOLTZ EQUATIONS; HIGH ORDER COMPACT SOLVERS;

FINITE DIFFERENCE METHOD;

EID: 33847400963     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2006.03.008     Document Type: Article

References (11)

1. A Maple module calculating symbolically composite finite difference expressions may be obtained from the author via request.
2. Ames W.F. Numerical Methods for Partial Differential Equations (1977), Academic Press, New York
3. Boisvert R.F. SIAM J. Sci. Statist. Comput. 2 (1981) 268
4. During the refereeing procedure the author was informed about a new work on sixth order schemes for the Helmholtz equation in two dimensions, based on a similar derivation than the present one: I. Singer, E. Turkel. Sixth order finite difference schemes for the Helmholtz equation, J. Comput. Acoust. (in press).
5. Harari I., and Turkel E. Accurate finite difference methods for time-harmonic wave propagation. J. Comput. Phys. 119 (1995) 252-270
6. Houstis E.N., and Papatheodorou T.S. In: Vichnevetsky R. (Ed). Advances in Computer Methods for Partial Differential Equations vol. II (1977), IMACS, New Brunswick, NJ 46-52
7. Manohar R.P., and Stephenson J.W. Single cell high order difference methods for the Helmholtz equation. J. Comput. Phys. 51 (1983) 444-453
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11. G. Sutmann, B. Steffen, High-order compact solvers for the three dimensional Poisson equation. J. Comput. Appl. Math. 187 (2006) 142-170.