Numerical method of lines for first order partial differential equations with deviated variables

• Autorzy: Czernous W.
• Języki publikacji: EN

Abstrakty

EN

Classical solutions of nonlinear initial boundary value problems are approximated in the paper by solutions of suitable quasilinear differential difference systems. The proof of the stability of the method of lines is based on a comparison technique with nonlinear estimates of the Perron type. Numerical examples are given.

Słowa kluczowe

EN

initial boundary value problems; differential inequalities; interpolating operators; stability and convergence

PL

nierówności różniczkowe; zagadnienia brzegowe; operatory interpolacyjne

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2005
• Tom: Vol. 38, nr 1
• Strony: 239--254
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Czernous W.

• Gdańsk University of Technology, Department of Differential Equations, 11-12 Gabriel Narutowicz Street, 80-952 Gdańsk, Poland

Bibliografia

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• [3] M. Cinquini Cibrario, Sopra una classe di sistemi di equazioni nonlineari a derivate parziali in piu variabli indipendenti, Ann. Mat. Pura et Appl. 140 (1985), 223-253.
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• [5] Z. Kamont, S. Zacharek, The lines method for parabolic differential functional equations with initial boundary conditions of Dirichlet type, Atti. Sem. Mat. Fis. Univ. Modena 35 (1987), 249-262.
• [6] Z. Kamont, Hyperbolic Fuctional Differential Inequalities and Applications, Kluwer Acad. Publ., Dordrecht, Boston, London, 1999.
• [7] S. Łojasiewicz, Sur problèmes de Cauchy pour les systèmes d'équations aux dérivées partielles du premier ordre dans le cas hyperbolique de deux variables indépendantes, Ann. Polon. Math. 3 (1956), 87-117.
• [8] K. Schmit, R. Thompson and W. Walter, Existence of solutions of a nonlinear boundary value problem via method of lines, Nonlin. Anal., TMA (1978), 519-535.
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• [10] Wei Dongming, Existence, uniqueness and numerical analysis of solutions of a quasilinear parabolic problem, SIAM J. Numer. Anal. 29 (1992), 484-497.
• [11] A. V. Wouwer, Ph. Saucez, W. E. Schiesser, Adaptive Method of Lines, Boca Raton-London, Chapman and Hall/CRC, 2001.
• [12] S. Yuan, The Finite Element Method of Lines, Beijing, Science Press, 1991.