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In this paper convection-dominated problem is considered. The problem will lead to large oscillation since the coefficient of diffusion term is small. Firstly, the analytical solution is decomposed into the smooth component and the singular component. Secondly, Runge-Kutta method is applied to solve the equation outside the boundary layer. Thirdly, Petrov-Galerkin finite element method with piecewise-exponential...
In this paper the equation with periodical condition and small parameter is considered. The equation will lose boundary condition and lead to large oscillation in boundary layer. The properties of the equation is studied firstly. The analytical solution is decomposed into the smooth component and the singular component. The asymptotic solution is proposed secondly. The asymptotic solution is used...
Ordinary differential equation with small parameter is considered in this paper. This kind of problem changes rapidly in both side of boundary layer. Firstly, the asymptotic solution of the problem is presented in order one. The asymptotic solution is used to solve the problem outside the boundary layer. Secondly, the analytical solution is decomposed into the smooth component and the singular component...
Model with small parameter is considered. Such problem undergo rapid changes within the boundary layer since the presence of the small parameter. Firstly, the analytical result of the problem is studied. The bound of the analytical solution is presented by Gronwall inequality. Secondly, the analytical solution is decomposed into the computational component and the small component. It is proved to...
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