The Infona portal uses cookies, i.e. strings of text saved by a browser on the user's device. The portal can access those files and use them to remember the user's data, such as their chosen settings (screen view, interface language, etc.), or their login data. By using the Infona portal the user accepts automatic saving and using this information for portal operation purposes. More information on the subject can be found in the Privacy Policy and Terms of Service. By closing this window the user confirms that they have read the information on cookie usage, and they accept the privacy policy and the way cookies are used by the portal. You can change the cookie settings in your browser.
Periodical problem is of common occurrence in many applied fields. In this paper the equation with periodical condition and small parameter is considered. The problem will lead to large oscillation since the parameter is small. The boundary layer function is presented firstly. The smooth component is constructed by the boundary layer function secondly. The error estimation of analytical solution is...
Model with small parameter and Robin boundary condition is considered. This is a multi-scale problem. The presence of small parameter leads to boundary layer phenomena. In order to discrete robin boundary condition and improve the order of uniform convergence, first transition point, which is very small, is introduced firstly. The domain is divided into the inner boundary layer region and the outside...
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...
Parabolic partial differential equation with periodical boundary value condition is considered. The equation also contains small parameter in x direction and different small parameter in t direction. The present of small parameter leads to boundary layer phenomena in both side of x direction and bottom side of t direction. The solution changes rapidly near three boundary layer. Left boundary layer...
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...
Parabolic partial differential equation with small parameter in x direction and different small parameter in t direction is considered. This kind of problem leads to boundary layer phenomena in both side of x direction and bottom side of t direction. The analytical solution changes rapidly near three boundary layer. Firstly, the asymptotic solution with order one for all small parameter is studied...
Set the date range to filter the displayed results. You can set a starting date, ending date or both. You can enter the dates manually or choose them from the calendar.