- 作者: 陳木陽; 黃奇
- 作者服務機構: 國立成功大學化學工程學系
- 中文摘要:
本文利用轉移式 Chebyshev 多項式解線性兩點邊界值問題。文中首先將含兩點邊界條件之微分方程式轉換成僅含起
始值之汎函微分方程式;然後利用轉移式 Chebyshev 多項式及其積分運算矩陣,將此汎函微分方程式轉換成聯立代數方
程式;再利用推導出的遞?演算法計算未知係數。
T - 英文摘要: The shifted Chebyshev polynomials are applied to solve a set of simultaneous first-order linear dif-ferential equations of constant coefficients with the given conditions being specified at two differentpoints. The approach adopted is that of transforming the two-point boundary value problem into a set offunctional differential equations in which the given conditions are all specifed at a single point. The set oftransformed functional differential equations is then solved by using the shifted Chebyshev polynomialsalong with the operational matrix of integration. A recursive algorithm is derived for computing theunknown coefficients with greatly reduced computational effort. Two examples are included to illustrateapplicability of the method.
- 中文關鍵字: orthogonal polynomials; Chebyshev polynomials; two-point boundary value problems
- 英文關鍵字: --