本研究主要探討內容為：1.取12個函數進行Gaver-Stehfest公式之模擬誤差討論，2.利用簡單的變數轉改變Gaver-Stehfest公式之探討，3.應用於常微分方程時函數之局部計算及延伸探討。 經初步研究討論，利用Gaver-Stehfest公式之數值模擬時，對於振盪之函數有定性上的誤差；而利用簡單的變數轉換，透過時間平移觀念，其能夠減緩並延長模擬的效果；在常微分方程應用上，利用局部計算之方式，能減少誤差之產生，在延伸方面之探討，時間越長其所採之時間間隔須越小，方能減少誤差之產生。 This research includes the following issues：1.Investigating the simulation error induced by using the Gaver-Stehfest formula, 2.Improving the power of the Gaver-Stehfest formula by using some theorems about Laplace transform, 3.Investigating the application of the Gaver-Stehfest formula to differential equations. We found that when simulating the functions with oscillations the Gaver-Stehfest formula induced errors after one cycle of oscillation. This kind of drawback can be improved if we use some theorems about Laplace transform to reduce the error. When treating ODES we can extend the effective region of the Gaver-Stehfest formula by some technique of local extension.
