Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

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

 
 

 

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
DOI: https://doi.org/10.1090/S0025-5718-1982-0669640-6
MathSciNet review: 669640
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.
  • [3] Y. L. Luke, The Special Functions and Their Approximations, Vols. I and II, Academic Press, New York, 1969. MR 0241700 (39:3039)
  • [4] G. Meinardus, Approximation of Functions: Theory and Numerical Methods, Springer-Verlag, Berlin, 1967. MR 0217482 (36:571)
  • [5] E. L. Ortiz, "The Tau method," SIAM J. Numer. Anal., v. 6, 1969, pp. 480-492. MR 0258287 (41:2934)
  • [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)
  • [7] E. L. Ortiz, "Step by step Tau method," Comput. Math. Appl., v. 1, 1975, pp. 381-392. MR 0464550 (57:4480)
  • [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)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65L05

Retrieve articles in all journals with MSC: 65L05


Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1982-0669640-6
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

American Mathematical Society