A high-order difference scheme for a nonlocal boundary-value problem for the heat equation.
Sun, Zhi-Zhong (2001)
Computational Methods in Applied Mathematics
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Sun, Zhi-Zhong (2001)
Computational Methods in Applied Mathematics
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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...
Gordeziani, E., Gordeziani, D. (2000)
Bulletin of TICMI
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Florian Mehats (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
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We present here a discretization of a nonlinear oblique derivative boundary value problem for the heat equation in dimension two. This finite difference scheme takes advantages of the structure of the boundary condition, which can be reinterpreted as a Burgers equation in the space variables. This enables to obtain an energy estimate and to prove the convergence of the scheme. We also provide some numerical simulations of this problem and a numerical study of the stability of the...
Zdzisław Denkowski (1970)
Annales Polonici Mathematici
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Kenichi Arai, Ken Wakabayashi, Hiroyuki Okazaki (2014)
Formalized Mathematics
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In [11], the definitions of forward difference, backward difference, and central difference as difference operations for functions on R were formalized. However, the definitions of forward difference, backward difference, and central difference for functions on vector spaces over F have not been formalized. In cryptology, these definitions are very important in evaluating the security of cryptographic systems [3], [10]. Differential cryptanalysis [4] that undertakes a general purpose...
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...
Z. Kowalski (1965)
Annales Polonici Mathematici
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Tadeusz Rumak (1972)
Annales Polonici Mathematici
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Janusz Traple (1977)
Annales Polonici Mathematici
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