Chebyshev polynomial solutions of linear differential equations
Chebyshev polynomial solutions of linear differential equations
复制标题
线性微分方程的切比雪夫多项式解
DOI：
10.1080/0020739960270414
复制
发表时间：
1996
期刊：
影响因子：
--
通讯作者：
M. Kaynak
中科院分区：
文献类型：
--
作者：
M. Sezer;M. Kaynak
给出了一种用切比雪夫多项式近似求解线性微分方程的矩阵方法，称为切比雪夫矩阵方法。该方法首先取方程中函数的切比雪夫级数，然后将其矩阵形式代入给定的方程。因此，该方程简化为矩阵方程，其对应于具有未知切比雪夫系数的线性代数方程组。为了说明该方法，在给定的条件下，它被应用到某些线性微分方程，并比较结果。
A matrix method, which is called the Chebyshev‐matrix method, for the approximate solution of linear differential equations in terms of Chebyshev polynomials is presented. The method is based on first taking the truncated Chebyshev series of the functions in equation and then substituting their matrix forms into the given equation. Thereby the equation reduces to a matrix equation, which corresponds to a system of linear algebraic equations with unknown Chebyshev coefficients. To illustrate the method, it is applied to certain linear differential equations under the given conditions and the results are compared.