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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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$A$-stability of a class of methods for the numerical integration of certain linear systems of ordinary differential equations
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by M. R. Crisci and E. Russo PDF
Math. Comp. 38 (1982), 431-435 Request permission

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
    M. R. Crisci & E. Russo, "A class of methods for the numerical integration of certain linear systems of ordinary differential equations." (To appear.) C. Lanczos, "Trigonometric interpolation of empirical and analytical functions," J. Math. Phys., v. 17, 1938, pp. 123-199.
  • Leon Lapidus and John H. Seinfeld, Numerical solution of ordinary differential equations, Mathematics in Science and Engineering, Vol. 74, Academic Press, New York-London, 1971. MR 0281355
  • Morris Marden, The Geometry of the Zeros of a Polynomial in a Complex Variable, Mathematical Surveys, No. 3, American Mathematical Society, New York, N. Y., 1949. MR 0031114
  • Eduardo L. Ortiz, The tau method, SIAM J. Numer. Anal. 6 (1969), 480–492. MR 258287, DOI 10.1137/0706044
  • Eduardo L. Ortiz, Canonical polynomials in the Lanczos tau method, Studies in numerical analysis (papers in honour of Cornelius Lanczos on the occasion of his 80th birthday), Academic Press, London, 1974, pp. 73–93. MR 0474847
  • K. Wright, Some relationships between implicit Runge-Kutta, collocation Lanczos $\tau$ methods, and their stability properties, Nordisk Tidskr. Informationsbehandling (BIT) 10 (1970), 217–227. MR 266439, DOI 10.1007/bf01936868
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Additional Information
  • © Copyright 1982 American Mathematical Society
  • Journal: Math. Comp. 38 (1982), 431-435
  • MSC: Primary 65L07
  • DOI: https://doi.org/10.1090/S0025-5718-1982-0645660-2
  • MathSciNet review: 645660