第一类shifted chebyshev多项式用于最小二乘法分析正方形截面杆的扭转问题

Analysis of Square Section Bar-Twisting Problems by the Least Square Method with Shifted Chebyshev Polynomials of the First Kind as Trial Functions

本文介绍第一类Shifted Chebyshev多项式,求出它的微分运算矩阵。将任意平方可积函数用有限多个第一类Shifted Chebyshev多项式表示,利用运算矩阵和最小二乘法,使求解偏微分方的问题归结为求解代效方程组,因而求出正方形截面杆的扭转问题的数值解。该方法比较简单,其结果精确度较好。

In this paper, the shifted Chebyshev polynomials of the first kind are introduced and its operational matrix for the differentiation is developed. The candidate functions are expressed by shifted Chebyshev series of the first kind. The partial differential equation is reduced to solving algebraic equations by using the operational matrix and the least square method. The algebraic equations are solved to evaluate the computed solution of the square section bar-twisting problems. The computational algorithm is simple and the computational results are satisfied.