基于Legendre多项式函数系的齐次扩容精细算法  

A homogeneous high precise direct integration based on legendre polynomial series

作　　者：时小红[1] 周钢[1] 付召华[1] 

机构地区：[1]上海交通大学数学系,上海200240

出　　处：《计算力学学报》2005年第3期335-338,共4页Chinese Journal of Computational Mechanics

基　　金：国家自然科学基金(50376039);国家教育部科学技术重点项目资助项目.

摘　　要：基于Legendre多项式函数系的特点,设计了求解非齐次线性定常系统的一种新的精细算法——基于Legendre正交多项式系的齐次扩容精细算法(HHPD-L)。这一算法不仅避免了HPD-F算法中的矩阵求逆,还克服了HHPD-F算法中非齐次函数周期性要求的限制;不仅计算量小、设计合理,还易于推广和实现。两个典型算例表明,HHPD-L算法的数值结果更为理想。<Abstrcat> This article devises the method of HHPD-L(Homogenized High Precise Direct-Legendre) by employing the technology of homogenization and linearizing stimulus f(t) basing on Legendre Polynomial series within every τ, which avoids inversing matrixes from which HHPD-F suffers and increases efficiency greatly. Meanwhile, HHPD-L conquered the restriction that stimulus f(t) must be periodic or continuous, which HHPD-F and HHPD-T suffers respectively. In addition, HHPD-L has several other advantages, such as simpler in designing, easier to generalize and implement. Ad hoc, it can be used in any casses when the stimulus f(t) is a continuous fractional function, which broadens the range where this methods could be effective. The results of the two examples discussed in this paper show that the HHPD-L is more effective.

关 键 词：精细算法 非齐次动力系统 齐次扩容精细算法 

分 类 号：O241.4[理学—计算数学]