The development and extended applications of precise integration method
In 1991,ZHONG Wanxie first proposed the Precise Integration Method(PIM)for calculating matrix exponential,the main points of which are a 2N algorithm and increment storage.The PIM can give the precise solution of the matrix exponential in the computer sense and provide a high-precision stable algorithm for the numerical calculation of ordinary differential equations,and it has been successfully applied in many fields such as structural dynamics response,random vibration,heat conduction,optimal control.This paper first introduces the proposal,basic idea and development of PIM for matrix exponential calculation.Then various PIMs for solving time-invariant and time-varying linear differential equations,nonlinear differential equations and large-scale problems are presented,and their advantages,disadvantages and the range of application are also analyzed.Finally,the extended application of the basic idea of PIM for two-point boundary value problems,elliptic functions,ill-conditioned algebraic equations and other problems is described,which further demonstrates the characteristics of PIM.
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维普
