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$ A$-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), 431-435
MSC: Primary 65L07
DOI: https://doi.org/10.1090/S0025-5718-1982-0645660-2
MathSciNet review: 645660
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Abstract | References | Similar Articles | Additional Information

Abstract: This paper is concerned with the analysis of the stability of a class of one-step integration methods, originated by the Lanczos tau method and applicable to particular linear differential systems.

It is proved that these methods are A-stable for every order.


References [Enhancements On Off] (What's this?)

  • [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. 123-199.
  • [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. 480-492. 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 Runge-Kutta, collocation and Lanczos $ \tau $ methods, and their stability properties," BIT, v. 10, 1970, pp. 217-227. MR 0266439 (42:1345)

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1982-0645660-2
Article copyright: © Copyright 1982 American Mathematical Society

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