Generation of finite difference formulas on arbitrarily spaced grids

Author:
Bengt Fornberg

Journal:
Math. Comp. **51** (1988), 699-706

MSC:
Primary 65D25

MathSciNet review:
935077

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Abstract | References | Similar Articles | Additional Information

Abstract: 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).

**[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. MR**0167642****[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. MR**0421096****[4]**H. B. Keller and V. Pereyra,*Symbolic generation of finite difference formulas*, Math. Comp.**32**(1978), no. 144, 955–971. MR**0494848**, 10.1090/S0025-5718-1978-0494848-1**[5]**W. D. Lakin,*Differentiating matrices for arbitrarily spaced grid points*, Internat. J. Numer. Methods Engrg.**23**(1986), no. 2, 209–218. MR**831853**, 10.1002/nme.1620230205

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1988-0935077-0

Keywords:
Finite difference coefficients,
high-order accuracy

Article copyright:
© Copyright 1988
American Mathematical Society