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Numerical solution of systems of ordinary differential equations with the Tau method: an error analysis

Authors: J. H. Freilich and E. L. Ortiz
Journal: Math. Comp. 39 (1982), 467-479
MSC: Primary 65L05
MathSciNet review: 669640
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Abstract: The recursive formulation of the Tau method is extended to the case of systems of ordinary differential equations, and an error analysis is given.

Upper and lower error bounds are given in one of the examples considered. The asymptotic behavior of the error compares in this case with that of the best approximant by algebraic polynomials for each of the components of the vector solution.

References [Enhancements On Off] (What's this?)

  • [1] J. H. Freilich & E. L. Ortiz, Simultaneous Approximation of a Function and its Derivative with the Tau Method, Conf. on Numerical Analysis, Dundee, 1975 and Imperial College, NAS Res. Report, 1975, pp. 1-45.
  • [2] C. Lanczos, "Trigonometric interpolation of empirical and analytical functions," J. Math. Phys., v. 17, 1938, pp. 123-199.
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  • [6] E. L. Ortiz, "On the numerical solution of nonlinear and functional differential equations with the Tau method," in Numerical Treatment of Differential Equations in Applications (R. Ansorge and W. Törnig, Eds.), Springer-Verlag, Berlin and New York, 1978, pp. 127-139. MR 515576 (80c:65180)
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  • [8] E. L. Ortiz & H. Samara, "A new operational approach to the numerical solution of differential equations in terms of polynomials," in Innovative Numerical Analysis for the Engineering Sciences (R. Shaw and W. Pilkey, Eds.), The University Press of Virginia, Charlottesville, Va., 1980, pp. 643-652. MR 645356 (83i:65067)

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Keywords: Initial value problems, boundary value problems, systems of ordinary differential equations, simultaneous approximation of functions, Tau method, collocation methods
Article copyright: © Copyright 1982 American Mathematical Society

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