Analysis of the Spectral Stability of the Generalized Runge–Kutta Methods Applied to Initial-Boundary-Value Problems for Equations of the Parabolic Type. II. Implicit Methods

Author:

Yankovskii А. P.

Publisher

Springer Science and Business Media LLC

Subject

Applied Mathematics,General Mathematics,Statistics and Probability

Reference15 articles.

1. I. S. Berezin and N. P. Zhidkov, Computing Methods, Vol. 1, Addison-Wesley, Reading, MA; Pergamon Press, Oxford (1965).

2. K. Dekker and J. G. Verwer, Stability of Runge–Kutta Methods for Stiff Nonlinear Differential Equations, North-Holland, Amsterdam (1984).

3. H. S. Carslaw and J. C. Jaeger, Conduction of Heat in Solids, Clarendon Press, Oxford (1959).

4. Yu. V. Nemirovskii and A. P. Yankovskii, “Numerical integration of initial-boundary-value problems with high gradients of solution by the generalized Runge–Kutta methods,” Mat. Met. Fiz.-Mekh. Polya, 47, No. 1, 43–62 (2004).

5. A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, Integrals and Series, Vol. 1: Elementary Functions [in Russian], Nauka, Moscow (1981)

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