透過第三、四章的數值推導與算例，我們可以明顯的看到簡化的李代數矩陣 '
A 對於求解四階邊界值問題的結果。它可以非常容易的應用在李群打靶法上求 解樑振動的邊界值問題，並且此代數矩陣也解決了兩大問題，其一是非線性樑問 題難以被轉換為史特姆─李奧維爾方程式的困擾，第二是過去的李代數結構在指 數映射轉換上太過複雜的問題。由結果來看，不論是線性或是非線性的系統李群 SL(4,R)打靶法都有不錯的表現，其打法的精準度都可以到達積分步長的 1.5 次方 至 2.5 次方左右，加上一步保群算法本身在解決邊界值問題上便是一個非常有效 率、快速的方法，不難看出此數值計算方法的優秀之處。
與其優點相對的，是李群 SL(4,R)打靶法在求解邊界值問題時，儘管在邊界 上的打靶目標有不錯的打靶精度，但其求解出來的初始值所積分出來的函數在邊 界以外的中段區域，其誤差值與邊界相差甚大，此點在算例一中可以發現。除此 之外在第三章中我們提到，簡化李代數矩陣A'必須經過一個適當的變數變換來 避免無法計算或是減根的問題，但是此變數變換一來會增加我們計算時所需要給 定的參數數量與數值疊代次數，讓打靶法的效率下降，二來則是在求解特徵值問 題時，因為變數變換後的方程式已不再是特徵方程式，所以不但求解出的特徵值 λ與使用史特姆─李奧維爾方程式的特徵值不相同，其對應的樑振態也因此而產 生些微的改變。
由結果來看，運用簡化後的李代數矩陣所做的李群 SL(4,R)打靶法在應用效 率與計算複雜度上，都勝過過往所使用的李群打靶法，但是在精度方面簡化的李 代數矩陣則無法達到同樣的高度。究其原因仍是因為簡化的李代數矩陣將所有的 變數都集中於一個函數內，因此而大大縮短了計算推導的複雜性，相對地自然在 精度上無法跟變數分離的舊李群打靶法相比。儘管如此，簡化過的李群打靶法其
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精度仍然維持著不錯的水準，但是在可應用的方程式層面卻廣非常多。故我們認 為這仍然是一個相當不錯的結果，對於需要以數值分析方法求解此類型邊界值問 題的工程師來說，李群 SL(4,R)打靶法是個簡單而高效率的方法，並且可以有效 解決複雜的結構元件計算及邊界值問題。不論是以求解微分方程的數值觀點來看，
亦或者是用工程師的角度來看，李群 SL(4,R)打靶法都是個相當有效並深具發展 潛力的數值計算方法。
本篇論文只探究了少數的四階微分方程式邊界值問題，但李群 SL(4,R)打靶 法事實上應用的層面更寬廣也更多元，不只是用於求解結構工程問題。對於其他 的物理問題如流體邊界層問題、熱流問題等等，期待之後的研究可以將此數值方 法應用於更多的方程式上，並且進一步改良李群元素與李代數的代數構造，讓打 靶法更加的精準、有效率。
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