Generation of finite difference formulas on arbitrarily spaced grids
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).
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M. Abramowitz & I. A. Stegun, Handbook of Mathematical Functions, National Bureau of Standards, Appl. Math. Series, no. 55, Washington, D. C., 1964.
S. J. Cynar, "Using Gaussian elimination for computation of the central difference equation coeficiente," SIGNUM Newsl. (USA), v. 22, 1987, pp. 12-19.
B. Fornberg, "On a Fourier method for the integration of hyperbolic equations," SIAM J. Numer. Anal., v. 12, 1975, pp. 509-528.
H. B. Keller & V. Pereyra, "Symbolic generation of finite difference formulas," Math. Comp., v. 32, 1978, pp. 955-971.
W. D. Lakin, "Differentiating matrices for arbitrarily spaced grid points," Internat. J. Numer. Methods Engrg., v. 23, 1986, pp. 209-218.
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