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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
MathSciNet review: 645660
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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.

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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.) 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
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  • 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

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Article copyright: © Copyright 1982 American Mathematical Society