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A Finite Difference Method for BBM-Burgers Equations

Author: WuWei
Tutor: ZhangLuMing
School: Nanjing University of Aeronautics and Astronautics
Course: Computational Mathematics
Keywords: BBM-Burgers equations finite difference scheme convergence stability
CLC: O241.8
Type: Master's thesis
Year: 2007
Downloads: 126
Quote: 1
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In this paper, the finite difference method for the homogenous initial boundary value problem of BBM-Burgers equations is considered. The main idea of the finite difference method is as follows: We consider the discrete differential equation with the continuous variant and boundary conditions. And the numerical solutions of difference equation are regarded as the approximate solutions for the differential equation.Firstly, A two-level difference scheme and a three-level difference scheme are proposed for BBM-Burgers equations in this paper. The error estimates are proved in theory. And, on the basis of priori estimate, convergence and stability of the difference solutions are proved by discrete functional analysis method. At last, numerical results demonstrate that the method is efficient and reliable. Furthermore, one finite difference scheme for generalized BBM-Burgers equations are also considered. The error estimates, convergence and stability of the difference solutions are proved .The difference method is also applicable to the periodic problem of BBM-Burgers equations, the initial-boundary problems of higher dimensional BBM-Burgers equations.

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CLC: > Mathematical sciences and chemical > Mathematics > Computational Mathematics > Numerical Analysis > The numerical solution of differential equations, integral equations
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