The Analysis Of Solution To The Dirichlet Problem With Scalariform Spacial Contrast Structure And It's Numerical Method

In this paper, we analyze the Dirichlet problem which has typical scalariform spacial contrast structure by using the boundary layer function method in the first and at the same time we constructed the approximate solution of the problem. Then on the basis of this theory we mainly use the Differential Quadrature Method (DQM) to get the numerical approximate solution. High precision, easily handle with the boundary conditions are the advantages of this method propounded by Bellman. We would get the approximate solution with less computation by using the DQM.We divide the interval of the Dirichlet problem into three parts near the turning point, so that the problem can be simplified and in each subinterval the problem will merely be of boundary layer. Then we will get the approximate solution to the problem in each subinterval by using DQM. Finally, the complete approximate solution to Dirichlet problem will be obtained through smoothly connect condition among the connected points of each subinterval.