An Artificial Boundary Method For Burgers' Equation In Infinite Two-dimensional Domains

In this thesis, by the theory of the natural boundary reduction, an artificial boundary method for Burgers' equation in infinite two-dimensional domains is considered. The main work of this thesis is as follows.Firstly, based on the Cole-Hopf transformation, the Burgers'equation is changed into a heat conduction equation. Secondly, a circular artificial boundary is introduced, then the original unbounded domain is decomposed into a bounded subdomain and an exterior unbounded subdomain outside the artificial boundary, and exact and approximate artificial boundary conditions are obtained on circu-lar artificial boundary by the Fourier method. Thirdly, we propose an exact or approximate boundary condition to reduce the given problem an initial-boundary value problem of heat equation in the finite computational subdomain, which is equivalent to the original problem and analysis the stablity of the equivalent prob-lem. Finally, the reduced problem is to solved by the finite difference method. Some numerical examples are presented to show the feasibility and effectiveness of the method given in this thesis.