本論文的主題是介紹用數值譜方法對動作電位傳播問題的建構方式，對此類問題的wellposeness分析及計算格式的穩定性皆有討論。

　　對本類問題我們先尋找邊界條件的形式，進而運用數值譜方法建構其格式，以解動作電位在神經軸索及心肌組織上的傳播行為。對於基礎模型類的問題，本計算格式皆可成功的模擬動作電位的傳播，且與其他研究所獲得結果一致。最後，我們對此格式在求解實際的動作電位問題提出一些建議。

　In this thesis a general framework of constructing multidimensional pseudospectral schemes for simulating action potential wave propagating on excitable membranes.
Issues related to the wellposeness of the problems and to the stability of the schemes are emphasized especially. Our approach starts from the analyzing such wave problems and wellposed boundary operators are identified. We then employ pseudospectral penalty formulations to construct computational schemes for　solving problems such as traveling solutions of a nerve impulse propagating on axon fibers and action potential waves propagating on cardiac tissues. Issues related to the stability of the schemes are analyzed and discussed in details. Our main result is that the schemes are stable in the discrete $L_2$ norm at the semidiscrete level. The performances of the schemes are illustrated through numerical results computed by the schemes for model problems, and our results agree with those computed by other research groups. Issues related to the complexities involved in realistic computations and suggestions for conducting such problems are discussed as well.

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