Stability of Parabolic Difference Schemes in the Maximum Norm.
O.B. WIDLUND (1966)
Numerische Mathematik
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O.B. WIDLUND (1966)
Numerische Mathematik
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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.
Andrzej Karafiat (1991)
Annales Polonici Mathematici
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D.G. ARONSON (1963)
Numerische Mathematik
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Ashyralyev, A. (2007)
Mathematical Problems in Engineering
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A. Fitzke (1970)
Annales Polonici Mathematici
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T. Lewiński (1984)
Applicationes Mathematicae
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A. Poliński (2006)
Annales Polonici Mathematici
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We study the initial-value problem for parabolic equations with time dependent coefficients and with nonlinear and nonlocal right-hand sides. Nonlocal terms appear in the unknown function and its gradient. We analyze convergence of explicit finite difference schemes by means of discrete fundamental solutions.
Ashyralyev, A., Karatay, I., Sobolevskii, P.E. (2004)
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...
Rudolf Gorenflo (1983)
Annales Polonici Mathematici
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K. Kropielnicka (2007)
Annales Polonici Mathematici
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Nonlinear parabolic functional differential equations with initial boundary conditions of the Neumann type are considered. A general class of difference methods for the problem is constructed. Theorems on the convergence of difference schemes and error estimates of approximate solutions are presented. The proof of the stability of the difference functional problem is based on a comparison technique. Nonlinear estimates of the Perron type with respect to the functional variable for given...
Ashyralyev, Allaberen, Sozen, Yasar, Sobolevskii, Pavel E. (2007)
Abstract and Applied Analysis
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Bosko S. Jovanovic (1989)
Numerische Mathematik
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A. Fitzke (1970)
Annales Polonici Mathematici
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Raimondas Čiegis, Aleksas Mirinavičius (2011)
Open Mathematics
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We consider the accuracy of two finite difference schemes proposed recently in [Roy S., Vasudeva Murthy A.S., Kudenatti R.B., A numerical method for the hyperbolic-heat conduction equation based on multiple scale technique, Appl. Numer. Math., 2009, 59(6), 1419–1430], and [Mickens R.E., Jordan P.M., A positivity-preserving nonstandard finite difference scheme for the damped wave equation, Numer. Methods Partial Differential Equations, 2004, 20(5), 639–649] to solve an initial-boundary...
Sahimi, Mohd Salleh, Alias, Norma, Mansor, Noreliza Abu, Nor, Norhalena Mohd (2003)
Bulletin of the Malaysian Mathematical Sciences Society. Second Series
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