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

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.