Solving Steady State Two Dimensional Boundary Value Problems Involving Heat Distributions by Difference Equation Method

二維穩態熱傳導邊界值問題的差分方程式解法

樂文全(Wen-Chyuan Yueh)

《勤益學報》 22卷1期 (2004/06) Pp. 17-27

https://doi.org/10.6753/CYJ.200406.0017

摘要

差分方程式在離散動力系統中有許多之應用。筆者在前篇中已成功地利用差分方程式的方法解出了一維的熱傳導方程式邊界值問題。本文進一步利用差分方程式求得穩態二維熱傳導方程式的邊界值問題。其解在形式上與利用微分方程式的方法解出者甚為接近，而計算過程則較為簡單。

並列摘要

Difference equations have many applications in discrete dynamical system [1,2]. In the previous article [3], the author has successfully solved the (one dimensional) boundary value problems involving heat distributions in lumped rods by difference equation method. In this paper, the author extends this method to solve the two dimensional problems, and find that the results are very near to that obtained by differential equation method in forms, and is relatively simpler to that by the later.

並列關鍵字

Double sequence ； convolution product ； orthogonality ； difference equation ； heat transfer equation