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Тезисы докладов

Численное решение дифференциальных и интегральных уравнений

The purpose of our work is to consider scheme for which dominant process is the useful property. Such schemes belong to a class of partly-implicit schemes. Dynamic convection-diffusion equation in the incompressible environment was used for investigation. The standard 5-point pattern on the regular mesh was applied for approximation the differential equation. The linear algebraic equations system obtained after approximation was solved by GMRES(10) without preconditioner. Two partly-implicit schemes were considered. For each one the condition of stability was formulated. The standard mathematical formulas based on the theory of operators in finite-dimensional Hilbert space was applied for investigation. To show efficiency of partly-implicit schemes numerical results were compared with classical implicit scheme. We estimated stability, relative error and number of GMRES(10) iterations on the first timestep. The results obtained during research allow us to make a conclusion on efficient use of partly-implicit schemes for problems with dominant process.

Примечание. Тезисы докладов публикуются в авторской редакции

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