Abstract
For the case of Hermitian interpolation, we consider the approximation-iterative method introduced by Dzyadyk. We construct a practical algorithm.
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REFERENCES
V. K. Dzyadyk, Approximation-Iterative Method for the Approximate Solution of the Cauchy Problem for Ordinary Differential Equations [in Russian], Preprint No. 27, Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1984).
V. K. Dzyadyk and Yu. I. Romanenko, Approximation-Iterative Method for the Polynomial Approximation of Solutions of a Nonlinear Cauchy Problem for Equations of Hyperbolic Type [in Russian], Preprint No. 63, Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1986).
V. K. Dzyadyk, A. M. Basov, and M. M. Rizk, Theory and Application of the Approximation-Iterative Method and Its Comparison with Methods of the Runge — Kutta Type [in Russian], Preprint No. 39, Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1991).
V. K. Dzyadyk and Ya. F. Vasilenko, Application of the Approximation-Iterative Method to the Solution of Stiff Problems for Ordinary Differential Equation [in Russian], Preprint No. 55, Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1991).
V. K. Dzyadyk, Approximation Methods for Solutions of Differential and Integral Equations, VSP, Netherlands, Japan (1995).
L. E. Él'sgol'ts, Differential Equations and Calculus of Variations [in Russian], Mir, Moscow (1970).
M. M. Rizk, “Expansions for the fundamental Hermite interpolation polynomials in terms of Chebyshev polynomials,” Ukr. Math. Zh., 53, No. 1, 135–143 (2001).
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Rizk, M.M. Dzyadyk's Technique for Ordinary Differential Equations Using Hermitian Interpolating Polynomials. Ukrainian Mathematical Journal 53, 569–583 (2001). https://doi.org/10.1023/A:1012374520898
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DOI: https://doi.org/10.1023/A:1012374520898