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Computation of differentiating matrices for classical orthogonal polynomials of continuous and discrete argument

  • Numerical Methods of Solution of Equations
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Abstract

Recurrences are derived for computing the elements of the differentiating matrix for classical orthogonal polynomials of continuous and discrete argument. Two approaches to construction of difference differentiation formulas are considered. Examples of differentiating matrices for Hahn and Chebyshev orthogonal polynomials of discrete argument are given.

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References

  1. I. P. Natanson, Constructive Theory of Functions [in Russian], Moscow—Leningrad (1949).

  2. A. F. Nikiforov, S. K. Suslov, and V. B. Uvarov, Classical Orthogonal Polynomials of Discrete Variable [in Russian], Moscow (1985).

  3. A. F. Nikiforov and V. B. Uvarov, Special Functions of Mathematical Physics [in Russian], Moscow (1978).

  4. V. A. Chirikalov, Some Approximate Methods of Solution of Second-Order Equations of Mathematical Physics with Discontinuous Coefficients [in Russian], dissertation, Kiev (1982).

  5. V. A. Chirikalov, Generalized Matrix Formulas of Numerical Differentiation [in Russian], Kiev (1988). Unpublished manuscript, UkrNIINTI 15.06.88, No. 1506 Uk88.

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Authors and Affiliations

  1. Kiev University, Ukraine

    V. A. Chirikalov

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  1. V. A. Chirikalov
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Translated from Vychislitel'naya i Prikladnaya Matematika, No. 73, pp. 19–24, 1992.

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Chirikalov, V.A. Computation of differentiating matrices for classical orthogonal polynomials of continuous and discrete argument. J Math Sci 71, 2637–2641 (1994). https://doi.org/10.1007/BF02114036

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  • DOI: https://doi.org/10.1007/BF02114036

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