本文是利用LADM (Laplace Adomian Decomposition Method)結合Padé近似法來分析Falkner-Skan在二維層流的速度分布，進一步的改變楔型板的角度探討各角度的速度圖與文獻比對，另外也利用此方法分析溫度場與Falkner-Skan邊界層問題，改變Pr (Prandtl numbers)以及楔型板角度的溫度圖與文獻作比較。
Laplace Adomian分解法是由George Adomian教授提出的ADM法與Laplace轉換結合而成，而Laplace Adomian分解法的近似解為一個無窮多項的級數解，必須將方程式取至無窮多項否則不論求取多少分項仍屬於一片段級數解，此問題會導致發散無法收斂，然而結合Padé近似法可以修正此問題使解更為精準，此方法可以不用把邊界值問題轉換為初始值問題，使其解更為簡單快速。本文使用的Laplace Adomian結合Padé近似混合法針對不同角度楔型板的流體速度分布，以及不同角度與Pr數的溫度分布所計算的結果，與文獻中不同方法的數值解作比較，結果相當準確，由此可得知Laplace Adomian結合Padé近似混合法是準確且快速的方法。

The Laplace Adomian decomposition method is employed in the solution of the two dimensional laminar boundary layer of Falkner-Skan equation for wedge. And use this paper method to investigate the temperature field associated with the Falkner-Skan boundary equation.
The Laplace Adomian decomposition method combines the numerical Laplace transform algorithm and the Admoian decomposition method. The truncated series solution solved by the LADM diverges rapidly as the applicable domain increases. However, the Padé approximant extends the domain of the truncated series solution to obtain better accuracy and convergence. In this paper, a hybrid method of the LADM combined with the Padé approximant, named the hybrid Laplace Adomian decomposition method is proposed to solve the Falkner-Skan equation to demonstrate efficient and reliable results.
The LADM-Padé approximant solutions demonstrate efficient and reliable results and have been shown a good accuracy and convergence in comparison with the exact solutions and other numerical method solutions.

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