Displaying similar documents to “A difference method for a non-linear parabolic differential equation without mixed derivatives”

Numerical approximations of parabolic differential functional equations with the initial boundary conditions of the Neumann type

Roman Ciarski (2004)

Annales Polonici Mathematici

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The aim of this paper is to present a numerical approximation for quasilinear parabolic differential functional equations with initial boundary conditions of the Neumann type. The convergence result is proved for a difference scheme with the property that the difference operators approximating mixed derivatives depend on the local properties of the coefficients of the differential equation. A numerical example is given.

Implicit difference schemes for mixed problems related to parabolic functional differential equations

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.

Multicomponent flow in a porous medium. Adsorption and Soret effect phenomena: local study and upscaling process

Serge Blancher, René Creff, Gérard Gagneux, Bruno Lacabanne, François Montel, David Trujillo (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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Our aim here is to study the thermal diffusion phenomenon in a forced convective flow. A system of nonlinear parabolic equations governs the evolution of the mass fractions in multicomponent mixtures. Some existence and uniqueness results are given under suitable conditions on state functions. Then, we present a numerical scheme based on a "mixed finite element"method adapted to a finite volume scheme, of which we give numerical analysis. In a last part, we apply an homogenization technique...