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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.78.

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An extension of Ortiz’ recursive formulation of the tau method to certain linear systems of ordinary differential equations
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by M. R. Crisci and E. Russo PDF
Math. Comp. 41 (1983), 27-42 Request permission

Abstract:

Ortiz’ step-by-step recursive formulation of the Lanczos tau method is extended to the numerical solution of linear systems of differential equations with polynomial coefficients. Numerical comparisons are made with Gear’s and Enright’s methods.
References
    C. A. Addison, Implementing a Stiff Method Based upon the Second Derivative Formulas, Tech. Rep. No. 130/79, University of Toronto, Dept. of Computer Science, 1979.
  • G. D. Byrne and A. C. Hindmarsh, A polyalgorithm for the numerical solution of ordinary differential equations, ACM Trans. Math. Software 1 (1975), no. 1, 71–96. MR 378432, DOI 10.1145/355626.355636
  • M. R. Crisci and E. Russo, $A$-stability of a class of methods for the numerical integration of certain linear systems of ordinary differential equations, Math. Comp. 38 (1982), no. 158, 431–435. MR 645660, DOI 10.1090/S0025-5718-1982-0645660-2
  • W. H. Enright, Second derivative multistep methods for stiff ordinary differential equations, SIAM J. Numer. Anal. 11 (1974), 321–331. MR 351083, DOI 10.1137/0711029
  • W. H. Enright, T. E. Hull & B. Lindberg, "Comparing numerical methods for stiff systems of O.D.E.: s," BIT, v. 15, 1975, pp. 10-48.
  • C. W. Gear, The automatic integration of stiff ordinary differential equations. , Information Processing 68 (Proc. IFIP Congress, Edinburgh, 1968) North-Holland, Amsterdam, 1969, pp. 187–193. MR 0260180
  • T. E. Hull, W. H. Enright, B. M. Fellen, and A. E. Sedgwick, Comparing numerical methods for ordinary differential equations, SIAM J. Numer. Anal. 9 (1972), 603–637; errata, ibid. 11 (1974), 681. MR 351086, DOI 10.1137/0709052
  • F. T. Krogh, "On testing a subroutine for the numerical integration of ordinary differential equations," Comm. ACM, v. 20, 1973, pp. 545-562. C. Lanczos, "Trigonometric interpolation of empirical and analytical functions," J. Math. Phys., v. 17, 1938, pp. 123-199.
  • Cornelius Lanczos, Applied analysis, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1956. MR 0084175
  • C. Lánczos, Legendre versus Chebyshev polynomials, Topics in numerical analysis (Proc. Roy. Irish Acad. Conf., University Coll., Dublin, 1972) Academic Press, London, 1973, pp. 191–201. MR 0341880
  • 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
  • Eduardo L. Ortiz, The tau method, SIAM J. Numer. Anal. 6 (1969), 480–492. MR 258287, DOI 10.1137/0706044
  • E. Ortiz, W. F. Pursuer & F. J. Canizares, Automation of the Tau Method, Report Math. Dept., University of London, 1972.
  • 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
  • E. L. Ortiz and H. Samara, An operational approach to the tau method for the numerical solution of nonlinear differential equations, Computing 27 (1981), no. 1, 15–25 (English, with German summary). MR 623173, DOI 10.1007/BF02243435
  • E. L. Ortiz, Step by step Tau method. I. Piecewise polynomial approximations, Computers and mathematics with applications, Pergamon, Oxford, 1976, pp. 381–392. MR 0464550, DOI 10.1016/0898-1221(75)90040-1
  • E. L. Ortiz, On the numerical solution of nonlinear and functional differential equations with the tau method, Numerical treatment of differential equations in applications (Proc. Meeting, Math. Res. Center, Oberwolfach, 1977) Lecture Notes in Math., vol. 679, Springer, Berlin, 1978, pp. 127–139. MR 515576
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Additional Information
  • © Copyright 1983 American Mathematical Society
  • Journal: Math. Comp. 41 (1983), 27-42
  • MSC: Primary 65L05; Secondary 65L07
  • DOI: https://doi.org/10.1090/S0025-5718-1983-0701622-9
  • MathSciNet review: 701622