Geodesic
Exponential difference schemes for solution of boundary problems for diffusion-convection equations
Matematičeskoe modelirovanie, Tome 28 (2016) no. 7, pp. 121-136

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The numerical solution of boundary-value problems is considered for multidimensional equations of convection-diffusion (CDE). These equations are used for many physical processes in solids, liquids and gases. A new approach to the spatial approximation for such equations is proposed. This approach is based on a integral transformation of second order differential operators. A linear version of CDE was selected to simplify analysis. For this variant, a new exponential difference schemes were offered, algorithms of its implementation were developed, a brief analysis of the stability and convergence was fulfilled. Numerical testing of approach was executed for a two-dimensional problem of metallic particles motion in the water flow under influence of a constant magnetic field.
Mots-clés : Convection-Diffusion Equation (CDE)
Keywords: Integral Transformation, Finite-Difference Schemes, Iterations, Non-monotonic sweep procedure. 
@article{MM_2016_28_7_a9,
     author = {S. V. Polyakov and Yu. N. Karamzin and T. A. Kudryashova and I. V. Tsybulin},
     title = {Exponential difference schemes for solution of boundary problems for diffusion-convection equations},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {121--136},
     publisher = {mathdoc},
     volume = {28},
     number = {7},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2016_28_7_a9/}
}
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S. V. Polyakov; Yu. N. Karamzin; T. A. Kudryashova; I. V. Tsybulin. Exponential difference schemes for solution of boundary problems for diffusion-convection equations. Matematičeskoe modelirovanie, Tome 28 (2016) no. 7, pp. 121-136. http://geodesic.mathdoc.fr/item/MM_2016_28_7_a9/