本文主要在探討一個管狀非絕熱反應器軸向分散模型的多重穩定狀態解。我們將提供一種演算法來求整個解路徑,並延拓隨著一個參數變動的多重穩定狀態解,稱之為虛擬弧長延拓法(pseudo-arclength continuation method)。虛擬弧長延拓法是基於打靶法、牛頓法、初始值解法、猜測及解法（predictor-solver）及隱函數定理等數值方法,且我們將利用其來探討軸向分散模型的多重穩定狀態解路徑。本文中,我們將藉由係數的改變,分歧圖的討論及多重穩定狀態解圖形的探討,並說明產生多重穩定狀態解的參數區間與初始條件的相互關係。

This thesis investigates the multiple steady state solutions of axial dispersion in a tubular non-adiabatic reactor model. In this study, a special algorithm is presented to find the whole solution path and to continue the multiple steady state solution path with different parameters. This is called pseudo-arclength continuation method, which is based on the shooting method, Newton’s method, Runge-Kutta method, predictor-solver and the implicit function theorem, of which we will make use to discuss the multiple steady state solution paths of axial dispersion model. In this study, we will observe the coefficient changes, discuss the bifurcation diagram of the multiple steady state solutions, and then explain the coefficient range of the multiple steady solutions as well as their correlations with the initial condition.

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