Displaying similar documents to “Non linear schemes for the heat equation in 1D”

Convergence of a numerical scheme for a nonlinear oblique derivative boundary value problem

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...

On some finite difference schemes for solution of hyperbolic heat conduction problems

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...

Finite volume schemes for the p-Laplacian on Cartesian meshes

Boris Andreianov, Franck Boyer, Florence Hubert (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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This paper is concerned with the finite volume approximation of the p-Laplacian equation with homogeneous Dirichlet boundary conditions on rectangular meshes. A reconstruction of the norm of the gradient on the mesh's interfaces is needed in order to discretize the p-Laplacian operator. We give a detailed description of the possible nine points schemes ensuring that the solution of the resulting finite dimensional nonlinear system exists and is unique. These schemes, called admissible,...