Numerical approximations of difference functional equations and applications

• Autorzy: Kamont Z.
• Języki publikacji: EN

Abstrakty

EN

We give a theorem on the error estimate of approximate solutions for difference functional equations of the Volterra type. We apply this general result in the investigation of the stability of difference schemes generated by nonlinear first order partial differential functional equations and by parabolic problems. We show that all known results on difference methods for initial or initial boundary value problems can be obtained as particular cases of this general and simple result. We assume that the right hand sides of equations satisfy nonlinear estimates of the Perron type with respect to functional variables.

Słowa kluczowe

EN

functional differential equations; stability and convergence; interpolating operators; nonlinear estimates of Perron type

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2005
• Tom: Vol. 25, no. 1
• Strony: 109--130
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Kamont Z.

• University of Gdańsk, Institute of Mathematics, Wit Stwosz Street 57, 80-952 Gdańsk, Poland,

Bibliografia

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• [3] Kamont Z.: Hyperbolic Functional Differential Inequalities and Applications. Dordrecht, Boston, London, Kluwer Acad. Publ. 1999.
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• [6] Reinhardt H.J.: Analysis of Approxiamtion Methods for Differential and Integral Equations. New York, Springer-Verlag 1985.
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• [8] Voigt W.: On finite-difference methods for parabolic functional-differential equ­ations on unbounded domains. Numerical Methods and Applications, 559-567, Sofia, Publ. House Bulg. Acad. Sci.1989.