Well-posedness of the boundary value problem for parabolic equations in difference analogues of spaces of smooth functions.
Ashyralyev, A. (2007)
Mathematical Problems in Engineering
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Ashyralyev, A. (2007)
Mathematical Problems in Engineering
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Ashyralyev, A., Karatay, I., Sobolevskii, P.E. (2004)
Discrete Dynamics in Nature and Society
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Ashyralyev, Allaberen, Gercek, Okan (2010)
Abstract and Applied Analysis
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Ashyralyev, Allaberen, Sirma, Ali (2009)
Discrete Dynamics in Nature and Society
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Crouzeix, Michel, Thomée, Vidar (2001)
Computational Methods in Applied Mathematics
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Ashyralyev, Allaberen, Sobolevskiĭ, Pavel E. (2006)
Discrete Dynamics in Nature and Society
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Milena Netka (2011)
Annales Polonici Mathematici
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Solutions of initial boundary value problems for parabolic functional differential equations are approximated by solutions of implicit difference schemes. The existence and uniqueness of approximate solutions is proved. The proof of the stability is based on a comparison technique with nonlinear estimates of the Perron type for given operators. It is shown that the new methods are considerably better than the explicit difference schemes. Numerical examples are presented.
Sobolevskii, Pavel E. (1997)
Discrete Dynamics in Nature and Society
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Ashyralyev, Allaberen, Gercek, Okan (2008)
Discrete Dynamics in Nature and Society
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Zdzisław Kamont, Karolina Kropielnicka (2012)
Annales Polonici Mathematici
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Initial-boundary value problems of Dirichlet type for parabolic functional differential equations are considered. Explicit difference schemes of Euler type and implicit difference methods are investigated. The following theoretical aspects of the methods are presented. Sufficient conditions for the convergence of approximate solutions are given and comparisons of the methods are presented. It is proved that the assumptions on the regularity of the given functions are the same for both...
Boško S. Jovanović (2007)
Kragujevac Journal of Mathematics
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Ashyralyev, A., Sobolevskii, P.E. (2001)
Abstract and Applied Analysis
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