Exact and Approximate Solutions to the Degenerated Reaction-Diffusion System
A. L. Kazakov1, L. F. Spevak2
1Matrosov Institute for System Dynamics and Control Theory Siberian Branch, Russian Academy of Sciences, Irkutsk, Russia
2Institute of Mechanical Engineering, Ural Branch, Russian Academy of Sciences, Ekaterinburg, Russia
Keywords: reaction-diffusion system, diffusion wave, exact solution, radial basis functions
Abstract
The problem of constructing solutions to a system of two coupled nonlinear parabolic equations of the reaction-diffusion type is considered. Solutions in the form of diffusion waves propagating over zero background with a finite speed are investigated. The theorem on the construction of exact solutions by reduction to the Cauchy problem for a system of ordinary differential equations is proved. A time-step numerical technique for solving the reaction-diffusion system using radial basis function expansion is proposed. The same approach is used to solve systems of ordinary differential equations that determine the exact solutions of the reaction-diffusion system. Numerical analysis and estimation of the accuracy of solutions to a system of ordinary differential equations are carried out. These solutions are applied to verify the obtained time-step solutions of the original system.
|
