Determination of an unknown parameter in a semi-linear parabolic equation.
Dehghan, Mehdi (2002)
Mathematical Problems in Engineering
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Dehghan, Mehdi (2002)
Mathematical Problems in Engineering
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Dehghan, Mehdi (2001)
Mathematical Problems in Engineering
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Liu, Don, Kuang, Weijia, Tangborn, Andrew (2009)
Advances in Mathematical Physics
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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...
Maria Antonietta Pirozzi (2001)
Rendiconti del Seminario Matematico della Università di Padova
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Raimund Bürger, Ricardo Ruiz, Kai Schneider, Mauricio Sepúlveda (2008)
ESAIM: Mathematical Modelling and Numerical Analysis
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We present a fully adaptive multiresolution scheme for spatially one-dimensional quasilinear strongly degenerate parabolic equations with zero-flux and periodic boundary conditions. The numerical scheme is based on a finite volume discretization using the Engquist-Osher numerical flux and explicit time stepping. An adaptive multiresolution scheme based on cell averages is then used to speed up the CPU time and the memory requirements of the underlying finite volume scheme, whose...
Kyei, Yaw, Roop, John Paul, Tang, Guoqing (2010)
Advances in Numerical Analysis
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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...
Franck Boyer, Sebastian Minjeaud (2011)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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In this article, we investigate numerical schemes for solving a three component Cahn-Hilliard model. The space discretization is performed by using a Galerkin formulation and the finite element method. Concerning the time discretization, the main difficulty is to write a scheme ensuring, at the discrete level, the decrease of the free energy and thus the stability of the method. We study three different schemes and prove existence and convergence theorems. Theoretical results are illustrated...