-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: 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]**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****[4]**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****[5]**Eduardo L. Ortiz,*The tau method*, SIAM J. Numer. Anal.**6**(1969), 480–492. MR**0258287**, https://doi.org/10.1137/0706044**[6]**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****[7]**K. Wright,*Some relationships between implicit Runge-Kutta, collocation Lanczos 𝜏 methods, and their stability properties*, Nordisk Tidskr. Informationsbehandling (BIT)**10**(1970), 217–227. MR**0266439**

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

Article copyright:
© Copyright 1982
American Mathematical Society