Abstract
The finite difference method such as alternating group iterative methods is useful in numerical method for evolutionary equations and this is the standard approach taken in this paper. Alternating group explicit (AGE) iterative methods for one-dimensional convection diffusion equations problems are given. The stability and convergence are analyzed by the linear method. Numerical results of the model problem are taken. Known test problems have been studied to demonstrate the accuracy of the method. Numerical results show that the behavior of the method with emphasis on treatment of boundary conditions is valuable.
Highlights
In this paper, we consider the one-dimensional time-dependent advection-diffusion equations= u∂∂u(t0= +,ta) ∂∂uxg1 ∂2u b ∂x2 (t),0 < x < L,0 < t < T 0
Equation (1) describes advection-diffusion of quantities such as heat, energy, mass, etc. They find their application in water transfer in soils, heat transfer in draining film, spread of pollutants in rivers and dispersion of tracers in porous media
Computational results are obtained to demonstrate the applicability of the method on some problems with known solutions
Summary
We consider the one-dimensional time-dependent advection-diffusion equations. Equation (1) describes advection-diffusion of quantities such as heat, energy, mass, etc They find their application in water transfer in soils, heat transfer in draining film, spread of pollutants in rivers and dispersion of tracers in porous media. As a major contribution for these mixed formulations, this method has overcome the difficulties concerning the usual stability conditions allowing combinations of simple finite element polynomials of almost any order including the attractive equal-order interpolations. They are important in many branches of engineering and applied science. In this paper we apply the AGE iterative method to the one-dimensional advection diffusion equation. Computational results are obtained to demonstrate the applicability of the method on some problems with known solutions
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