Series Solutions of Avoiding Calculating the Inverse of the State-Matrix for Nonlinear Dynamic Equation

摘要

Based on the precise integration method of the exponential matrix, we discuss a general dynamics system governed by the state-equation v = H·v + f(v,t). The nonlinear part f(v,t) can beexpressed in Taylor series at the time t_k . The authors suggest that the integral of the state-equation can be evaluated by numerical method directly through the exponential matrix and its precise algorithm, thus two kinds of series solutions can be successively obtained and the precision of the solutions can be controlled easily. Algorithms suggested avoid calculating the inverse of the matrix H and embody much more advantages when the inverse of the state-matrix H doesn't exist or approximate to be oddity, at the same time, the stabilization and efficiency of the computation can be ensured satisfactorily. The numerical examples are presented to demonstrate the validity of the two algorithms.