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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...
Time-dependent convection diffusion equation, with a discontinuous data and large Reynolds number, is examined. This kind of problem leads to interior layer phenomena due to the discontinuity. The solution changes rapidly near interior layer. Traditional finite volume method is applied. Two efficient numerical methods are constructed. One is Shishkin's finite volume method. Another is improved-Shishkin's...
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