×

zbMATH — the first resource for mathematics

Generation of finite difference formulas on arbitrary spaced grids. (English) Zbl 0701.65014
Summary: Simple recursions are derived for calculating the weights in compact finite difference formulas for any order of derivative and to any order of accuracy on one-dimensional grids with arbitrary spacing. Tables are included for some special cases (of equispaced grids).

MSC:
65D25 Numerical differentiation
26-04 Software, source code, etc. for problems pertaining to real functions
65A05 Tables in numerical analysis
65N06 Finite difference methods for boundary value problems involving PDEs
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Milton Abramowitz and Irene A. Stegun, Handbook of mathematical functions with formulas, graphs, and mathematical tables, National Bureau of Standards Applied Mathematics Series, vol. 55, For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C., 1964. · Zbl 0171.38503
[2] S. J. Cynar, ”Using Gaussian elimination for computation of the central difference equation coeficiente,” SIGNUM Newsl. (USA), v. 22, 1987, pp. 12-19.
[3] Bengt Fornberg, On a Fourier method for the integration of hyperbolic equations, SIAM J. Numer. Anal. 12 (1975), no. 4, 509 – 528. · Zbl 0349.35003 · doi:10.1137/0712040 · doi.org
[4] H. B. Keller and V. Pereyra, Symbolic generation of finite difference formulas, Math. Comp. 32 (1978), no. 144, 955 – 971. · Zbl 0387.65049
[5] W. D. Lakin, Differentiating matrices for arbitrarily spaced grid points, Internat. J. Numer. Methods Engrg. 23 (1986), no. 2, 209 – 218. · Zbl 0601.65013 · doi:10.1002/nme.1620230205 · doi.org
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.