具有任意激励的非齐次线性自治系统的齐次扩容精细算法

New homogenized high precision direct integration to solve non-homogeneous autonomy system with arbitrary stimulus

基于第二类Chebyshev多项式函数系的特点与齐次扩容技巧,设计了求解非齐次线性自治系统的一种新的长效精细算法(HHPD CS).其不仅避免了HPD F算法中的矩阵求逆,还克服了HH-PD 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.理论与算例表明,长效HHPD CS算法十分有效,不仅计算量比R K算法小许多,而且数值稳定、计算精度高、设计合理,易于推广和实现.

A new long-term-effective HPD method in short named HHPD-CS is devised to solve nonhomogeneous linear autonomy system based on Chebyshev orthogonal polynomials series of the second kind and homogenized integration technique. The algorithm can avoid inversing matrixes from which HPD-F suffers and conquer the restriction that stimulus must be periodic, from which HHPD-F suffers,so the method can be used for any kind of right stimulus. The results of the two examples discussed show that the long-term-effective HHPD-CS is more effective. In addition, HHPD-CS has several other advantages, such as simpler in designing and computational format, more precise, easier to be generalized and implemented etc.