基于Chebyshev多项式函数系的齐次扩容精细算法  

A Homogenized High Precision Direct Integration Based on Chebyshev Polynomial Series

作　　者：付召华[1] 周钢[1] 罗顺[1] 刘晓梅[1] 

机构地区：[1]上海交通大学数学系,上海200240

出　　处：《东华大学学报（自然科学版）》2006年第2期46-49,共4页Journal of Donghua University(Natural Science)

基　　金：国家自然科学基金项目(项目编号:50376039);受教育部科学技术研究重点项目的资助

摘　　要：基于Chebyshev多项式函数系的特点,设计了求解非齐次线性自治系统的一种新的精细算法———基于Chebyshev正交多项式系的齐次扩容精细算法(HHPDC)。这一算法不仅避免了HPD-F算法中的矩阵求逆,还克服了HHPDF算法中对右端激励的周期性要求,从而适合于任意形式的右端激励;不仅计算量小、设计合理,还易于推广和实现。理论与算例表明,HHPD-C算法十分有效。This article devises a new HPD method named HHPD- C to solve nonhomogeneous linear autonomy system basing on Chebyshev orthogonal Polynomial series. The algorithm avoids inversing matrixes from which HPD- F suffers and conquers the restriction that stimulus must be periodic, which HHPD- F suffers, so the method can be used for any stimulus. In addition, HHPD- C has several other advantages, such as simpler in designing, easier to generalize and implement. The results of the two examples discussed in this paper show that the HHPD- C is more effective.

关 键 词：精细算法 非齐次线性自治系统 齐次扩容精细算法 

分 类 号：O241.4[理学—计算数学]