臺灣博碩士論文加值系統

本研究首先利用泰勒定理形成偏導數的差分近似式，然後利用函數相鄰兩點泰勒級數展開式推導出含未定參數的三點有限差分通式，包括線性時的顯式與隱式三點差分通式及非線性時的三點差分通式。經由參數之設定，得到一些舊有差分法，及新的差分法，應用這些方法解三個一階雙曲線偏微分方程式例題並與正確解比較。

In the first place , this study is employed the Taylor's theorem informing difference approximations to first-order partial derivatives.Then , the Taylor's series expansion of a function is employed in theneighborhood of two points to derive the three point finite differenceformulas which consist of undetermined parameters and express inlinear and nonlinear formulation. By determining these parameters , it can get some old methods andsome new methods . Then , three examples of first-order hyperbolicpartial equation are performed to compare all existing methods with one another.