One method for solving systems of nonlinear partial differential equations |
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| Authors: | L I Rubina O N Ul’yanov |
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| Institution: | 1.Institute of Mathematics and Mechanics,Ural Branch of the Russian Academy of Sciences,Yekaterinburg,Russia;2.Institute of Radioelectronics and Information Technologies,Ural Federal University,Yekaterinburg,Russia |
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| Abstract: | A method for reducing systems of partial differential equations to corresponding systems of ordinary differential equations is proposed. A system of equations describing two-dimensional, cylindrical, and spherical flows of a polytropic gas; a system of dimensionless Stokes equations for the dynamics of a viscous incompressible fluid; a system of Maxwell’s equations for vacuum; and a system of gas dynamics equations in cylindrical coordinates are studied. It is shown how this approach can be used for solving certain problems (shockless compression, turbulence, etc.). |
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