對於二維拉普拉斯問題，本文利用分離變數法推導其級數解，再使用配點法來計算待定係數，並引入特徵長度的概念來提高求解的穩定性及精度。此方法在單連通、多連通區域均適用。邊界可以是任意形狀，並且對於內域、外域問題均可做計算。由數值計算的結果可以看出我們的方法有著很高的精度，對於邊界資料的擾動也有一定的穩定性。 In this paper we obtain the series solution by the separation of variables method for two-dimensional Laplace equation and calculate the coefficient of the series solution by the collocation method. We also introduce the characteristic length to improve the accuracy and the stability. This method can be used in both simply connected domain and multiply connected domain. The shape of boundary is arbitrary. This method can also be used in both interior problem and exterior problem. This method has high accuracy and stability even under the boundary data disturbance.