The precise time-integration method proposed for linear time-invariantdynamic system can give precise numerical results approaching to theexact solution at the integration points. However, it is more or lessdifficult when the algorithm is used to the non-homogeneous dynamicsystems due to the inverse matrix calculations. Precise time integrationwith dimensional expanding is proposed in the paper. By using thedimensional expanding, the non-homogeneous vector is viewed as thevariables of the equations and the original equations are converted intohomogeneous equations. Thus the new method avoids the inverse matrixcalculations and improves the computing efficiency. In particular, themethod is independent to the quality of the matrix . If the matrix is singular or nearly singular, the advantages of the method isremarkable. If the non-homogeneous vector is the solution of one ODEs,the method can give exact results. Otherwise, the methods of constant,linear or sinusoid approximation for the non-homogeneous vector can alsogive satisfying results. This new algorithm is not only benefit to boththe programming implementation and the numerical stability, but also moreefficient to large-scale problems. It has improved the precisetime-integration method. Numerical examples are given to demonstratethe validity and efficiency of the algorithm.%对线性定常结构动力系统提出的精细积分方法,能够得到在数值上逼近于精确解的结果,但是对于非齐次动力方程涉及到矩阵求逆的困难.提出采用增维的办法,将非齐次动力方程转化为齐次动力方程,在实施精细积分过程中不必进行矩阵求逆.这种方法对于程序实现和提高数值稳定性十分有利,而且在大型问题中计算效率较高,从而改进了精细积分方法的应用.数值例题显示了本文方法的有效性.
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