Abstract:
Object of this research are differential equations of diffusion-convection type. These equations are used for the description of many nonlinear processes in solids, liquids and gases. Despite a set of works on problems of their decision, they still present certain difficulties for the theoretical and numerical analysis. In the work the grid approach on the basis of the finite differences method for the solution of the equations of this kind is considered. For simplification of consideration the one-dimensional version of the equation was chosen. However the main properties of the equation are equal non-monotonicity and non-linearity were kept. For the solution of boundary problems for such equations the special variant of non-monotonic sweep procedure is offered.
Keywords:
diffusion-convection equation, finite-difference schemes, integral transformation, algorithm of non-monotonic sweep procedure.
Citation:
S. V. Polyakov, “Exponential finite-difference schemes with double integral transformation for desicion of diffusion-convection equations”, Mat. Model., 24:12 (2012), 29–32; Math. Models Comput. Simul., 5:4 (2013), 338–340
This publication is cited in the following 9 articles:
T. A. Kudryashova, S. V. Polyakov, “Flow Exponential Schemes for Solving Equation of Convection-Diffusion Type”, Math Models Comput Simul, 16:S2 (2024), S225
Miglena N. Koleva, Sergey V. Polyakov, Lubin G. Vulkov, Studies in Computational Intelligence, 1111, Advanced Computing in Industrial Mathematics, 2023, 112
Chernyshov A.D. Sajko D.S. Goryainov V.V. Kuznetsov S.F. Nikiforova O.Yu., “The Diffusion Problem in a Rectangular Container With An Internal Source: Exact Solutions Obtained By the Fast Expansion Method”, St. Petersb. Polytech. Univ. J.-Phys. Math., 13:3 (2020), 42–53
Sergey Polyakov, Tatiana Kudryashova, Nikita Tarasov, EngOpt 2018 Proceedings of the 6th International Conference on Engineering Optimization, 2019, 754
Karamzin Yu., Kudryashova T., Polyakov S., “On One Class of Flow Schemes For the Convection-Diffusion Type Equation”, Math. Montisnigri, 41 (2018), 21–32
Tatiana Kudryashova', Sergey Polyakov, Nikita Tarasov, N. Mastorakis, V. Mladenov, A. Bulucea, “A novel parallel algorithm for 3D modelling electromagnetic purification of water”, MATEC Web Conf., 210 (2018), 04027
Polyakov S.V., Karamzin Yu.N., Kudryasova T.A., Tarasov N.I., “Mathematical Modelling of Water Treatment Processes”, Math. Montisnigri, 40 (2017), 110–126
Sergey V. Polyakov, Yuri N. Karamzin, Tatiana A. Kudryashova, Viktoriia O. Podryga, Lecture Notes in Computer Science, 10187, Numerical Analysis and Its Applications, 2017, 550
S. V. Polyakov, Yu. N. Karamzin, T. A. Kudryashova, I. V. Tsybulin, “Exponential difference schemes for solution of boundary problems for diffusion-convection equations”, Math. Models Comput. Simul., 9:1 (2017), 71–82
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