Symbolic generation of finite difference formulas
HTML articles powered by AMS MathViewer
- by H. B. Keller and V. Pereyra PDF
- Math. Comp. 32 (1978), 955-971 Request permission
Abstract:
Tables of coefficients for high order accurate, compact approximations to the first ten derivatives on and at the midpoints of uniform nets are presented. The exact rational weights are generated and tested by means of symbolic manipulation implemented through MACSYMA. These weights are required in the application of deferred corrections to new methods for solving higher order two point boundary value problems.References
- C. Ballester and V. Pereyra, On the construction of discrete approximations to linear differential expressions, Math. Comp. 21 (1967), 297–302. MR 228167, DOI 10.1090/S0025-5718-1967-0228167-8
- Åke Björck and Victor Pereyra, Solution of Vandermonde systems of equations, Math. Comp. 24 (1970), 893–903. MR 290541, DOI 10.1090/S0025-5718-1970-0290541-1
- Eugene Isaacson and Herbert Bishop Keller, Analysis of numerical methods, John Wiley & Sons, Inc., New York-London-Sydney, 1966. MR 0201039 C. JORDAN, Calculus of Finite Differences, Chelsea, New York, 1947.
- H. B. Keller and V. Pereyra, Difference methods and deferred corrections for ordinary boundary value problems, SIAM J. Numer. Anal. 16 (1979), no. 2, 241–259. MR 526487, DOI 10.1137/0716018 MACSYMA, Reference Manual, The Mathlab Group, Project MAC, MIT, Boston, Mass., 1975.
- Milton Abramowitz and Irene A. Stegun, Handbook of mathematical functions with formulas, graphs, and mathematical tables, National Bureau of Standards Applied Mathematics Series, No. 55, U. S. Government Printing Office, Washington, D.C., 1964. For sale by the Superintendent of Documents. MR 0167642
- W. G. Bickley, Formulae for numerical differentiation, Math. Gaz. 25 (1941), 19–27. MR 3580, DOI 10.2307/3606475
- Bengt Fornberg, On a Fourier method for the integration of hyperbolic equations, SIAM J. Numer. Anal. 12 (1975), no. 4, 509–528. MR 421096, DOI 10.1137/0712040
Additional Information
- © Copyright 1978 American Mathematical Society
- Journal: Math. Comp. 32 (1978), 955-971
- MSC: Primary 65D25; Secondary 65B05, 65L10
- DOI: https://doi.org/10.1090/S0025-5718-1978-0494848-1
- MathSciNet review: 0494848