Approximation by aliasing with application to ``Certaine'' stiff differential equations
Authors:
Arthur David Snider and Gary Charles Fleming
Journal:
Math. Comp. 28 (1974), 465473
MSC:
Primary 65L99
MathSciNet review:
0343637
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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.
 [1]
R. W. Hamming, Introduction to Applied Numerical Analysis, McGrawHill, New York, 1971, pp. 287292.
 [2]
A. D. Snider, "An improved estimate of the accuracy of trigonometric interpolation," SIAM J. Numer. Anal., v. 9, 1972, pp. 505508. MR 0312682 (47:1238)
 [3]
J. Certaine, "The solution of ordinary differential equations with large time constants," in Mathematical Methods for Digital Computers, A. Ralston and H. S. Wilf (Editors), Wiley, New York, 1960, pp. 128132. MR 22 #8691. MR 0117917 (22:8691)
 [4]
K. G. Guderley & C.C. Hsu, "A predictorcorrector method for a certain class of stiff differential equations," Math. Comp., v. 26, 1972, pp. 5169. MR 45 #8001. MR 0298952 (45:8001)
 [5]
A. D. Snider, "A remark on a paper by Guderley and Hsu." (In prep.)
 [1]
 R. W. Hamming, Introduction to Applied Numerical Analysis, McGrawHill, New York, 1971, pp. 287292.
 [2]
 A. D. Snider, "An improved estimate of the accuracy of trigonometric interpolation," SIAM J. Numer. Anal., v. 9, 1972, pp. 505508. MR 0312682 (47:1238)
 [3]
 J. Certaine, "The solution of ordinary differential equations with large time constants," in Mathematical Methods for Digital Computers, A. Ralston and H. S. Wilf (Editors), Wiley, New York, 1960, pp. 128132. MR 22 #8691. MR 0117917 (22:8691)
 [4]
 K. G. Guderley & C.C. Hsu, "A predictorcorrector method for a certain class of stiff differential equations," Math. Comp., v. 26, 1972, pp. 5169. MR 45 #8001. MR 0298952 (45:8001)
 [5]
 A. D. Snider, "A remark on a paper by Guderley and Hsu." (In prep.)
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DOI:
http://dx.doi.org/10.1090/S00255718197403436373
PII:
S 00255718(1974)03436373
Article copyright:
© Copyright 1974
American Mathematical Society
