本文使用狀態變數與Hermite型置點之移動最小二乘方法分析波松方程式包括穩態熱傳與二維勢能流問題。在狀態變數法中於局部區域建立場量變數與其一階導數之近似函數，利用移動最小二乘法，考慮節點上近似函數之殘值與邊界之殘值及控制方程之殘值，建立加權殘值二次式，使其最小，可得含有狀態變數之節點值表示的近似函數，再利用狀態變數的節點值與近似函數在節點上之近似值須滿足一致性之條件，利用置點法建立聯立方程式求解，可一次求解出主要變數與其一階導數的節點值。Hermite型置點在局部區域只建立主要變數近似函數，建立加權殘值二次式時，一樣只考慮主要函數之殘值，再加上邊界之殘值及控制方程之殘值，使其最小，得含有主要變數的節點值表示之近似函數，且利用變數節點值與近似函數之節點值須滿足一致性，在置點的同時將其一階導數也考慮進去，一樣可一次求得主要變數與其一階導數近似函數節之點值。
本文數值範例中求解不同邊界條件之波松問題，並將求出之數值結果與解析解對照，驗證兩數值方法之精度及收斂率，並討論不同邊界條間對數值結果精度之影響。

In this paper, we use the moving least square methods based on state variables and Hermite type collocation to solve the two-dimensional Poisson's equations, including the steady-state heat transfer and potential flow problems. The core concepts of the two numerical methods discussed in this paper are similar to the idea of Moving Least Squares Methods. Considering about governing equations, boundary conditions, and the minimal weighted sum of the approximation of state variables, the values of the approximate functions can be obtained. As a result, the accuracy of the numerical results is great.
In the numerical examples, we solved Poisson's equations with various boundary conditions, and we compared the numerical results with exact solutions to examine the accuracy and the rate of convergence of the two methods. In this paper we also discuss the influence on numerical accuracy due to different boundary conditions.

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