Approximation by aliasing with application to “Certaine” stiff differential equations
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- by Arthur David Snider and Gary Charles Fleming PDF
- Math. Comp. 28 (1974), 465-473 Request permission
Abstract:
The usual method of finding an accurate trigonometric interpolation for a function with dominant high frequencies requires a large number of calculations. This paper shows how aliasing can be used to achieve a great reduction in the computations in cases when the high frequencies are known beforehand. The technique is applied to stiff differential equations, extending the applicability of the method of Certaine to systems with oscillatory forcing functions.References
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R. W. Hamming, Introduction to Applied Numerical Analysis, McGraw-Hill, New York, 1971, pp. 287-292.
- Arthur D. Snider, An improved estimate of the accuracy of trigonometric interpolation, SIAM J. Numer. Anal. 9 (1972), 505–508. MR 312682, DOI 10.1137/0709045
- J. Certaine, The solution of ordinary differential equations with large time constants, Mathematical methods for digital computers, Wiley, New York, 1960, pp. 128–132. MR 0117917
- Karl G. Guderley and Chen-chi Hsu, A predictor-corrector method for a certain class of stiff differential equations, Math. Comp. 26 (1972), 51–69. MR 298952, DOI 10.1090/S0025-5718-1972-0298952-7 A. D. Snider, "A remark on a paper by Guderley and Hsu." (In prep.)
Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Math. Comp. 28 (1974), 465-473
- MSC: Primary 65L99
- DOI: https://doi.org/10.1090/S0025-5718-1974-0343637-3
- MathSciNet review: 0343637