Increment-dimensional precise integration method for nonlinear dynamic equation

The precise integration method proposed for linear-invariant dynamic system can give precise numerical results approaching to the exact solution at the integration points. However, it is more or less difficult when the algorithm is used to the non-homogeneous dynamic system due to the inverse matrix calculations, and the non-homogeneous vector with relation to time variable do not be considered in the process of division of the precise integration. The original non-homogeneous equation is converted into homogeneous equation by means of increment-dimensional method. Then, precise integration method can be used and the inverse matrix need not be computed in the integration. The present method is not only benefit to both programming implementation and improving the numerical stability, but also more efficient to the large-scale problem. The numerical examples show the validity and efficiency of the method.