在扇形的拉普拉斯問題上我們任意給定常數的Dirichlet或Neumann邊界條件，大部分這種問題其解都會有奇異性質。一開始我們先分析在角點上的奇異類型且用一些已知的方法來檢視這些問題，我們使用邊界近似法(BAM)來計算一些有兩個奇異點的解，另外我們也用分離變數法來計算在三角形上有多組解的拉普拉斯問題。

In this thesis, we consider the Laplace quation on sector with various constant Dirichlet or Numann boundary conditions. Most of such problems have singularity in the solution. We first analyze the type of singularity on the corner and then survey some known methods to solve these problems. The boundary approximation method is used to compute some of their solutions with two singularities. Besides, a Laplace equation on a triangle with multiple solutions is solved by the method of separation of variables.

1.Introduction
2.Singularity Analysis
3.Triangular Model
4.NDN Model
5.NND Model
6.NDD model

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