-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.

**[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 methods, and their stability properties,"*BIT*, v. 10, 1970, pp. 217-227. MR**0266439 (42:1345)**

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DOI:
https://doi.org/10.1090/S0025-5718-1982-0645660-2

Article copyright:
© Copyright 1982
American Mathematical Society