基于Chebyshev多项式函数系的齐次扩容精细算法

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（HHPD-C）。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。理论与算倒表明，HHPD—C算法十分有效。

A Homogenized High Precision Direct Integration Based on Chebyshev Polynomial Series

This article devises a new HPD method named HHPDC to solve nonhomogeneous linear autonomy system basing on Chebyshev orthogonal Polynomial series. The algorithm avoids inversing matrixes from which HPDF suffers and conquers the restriction that stimulus must be periodic, which HHPDF suffers, so the method can be used for any stimulus. In addition, HHPDC 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 HHPDC is more effective.