stability of a class of methods for the numerical integration of certain linear systems of ordinary differential equations
Authors:
M. R. Crisci and E. Russo
Journal:
Math. Comp. 38 (1982), 431435
MSC:
Primary 65L07
MathSciNet review:
645660
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Abstract: This paper is concerned with the analysis of the stability of a class of onestep integration methods, originated by the Lanczos tau method and applicable to particular linear differential systems. It is proved that these methods are Astable for every order.
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M. R. Crisci & E. Russo, "A class of methods for the numerical integration of certain linear systems of ordinary differential equations." (To appear.)
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 [1]
 M. R. Crisci & E. Russo, "A class of methods for the numerical integration of certain linear systems of ordinary differential equations." (To appear.)
 [2]
 C. Lanczos, "Trigonometric interpolation of empirical and analytical functions," J. Math. Phys., v. 17, 1938, pp. 123199.
 [3]
 T. Lapidus & J. H. Seinfeld, "Numerical solution of ordinary differential equations," Mathematics in Science and Engineering, vol. 75, Academic Press, New York, 1971. MR 0281355 (43:7073)
 [4]
 M. Marden, The Geometry of the Zeros of a Polynomial in a Complex Variable, Math. Surveys, no. 3, Amer. Math. Soc., Providence, R. I., 1949. MR 0031114 (11:101i)
 [5]
 E. Ortiz, "The tau method," SIAM J. Numer. Anal., v. 6, 1969, pp. 480492. MR 0258287 (41:2934)
 [6]
 E. Ortiz, "Canonical polynomials in the Lanczos tau method," Studies in Numerical Analysis, Academic Press, London, 1974. MR 0474847 (57:14478)
 [7]
 K. Wright, "Some relationships between implicit RungeKutta, collocation and Lanczos methods, and their stability properties," BIT, v. 10, 1970, pp. 217227. MR 0266439 (42:1345)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718198206456602
PII:
S 00255718(1982)06456602
Article copyright:
© Copyright 1982
American Mathematical Society
