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Indexed by:期刊论文

Date of Publication:2013-01-01

Journal:APPLIED MATHEMATICS AND MECHANICS-ENGLISH EDITION

Included Journals:SCIE、EI

Volume:34

Issue:1

Page Number:1-14

ISSN No.:0253-4827

Key Words:differential Riccati equation (DRE); precise integration method (PIM); exponential of matrix; error analysis

Abstract:An improved precise integration method (IPIM) for solving the differential Riccati equation (DRE) is presented. The solution to the DRE is connected with the exponential of a Hamiltonian matrix, and the precise integration method (PIM) for solving the DRE is connected with the scaling and squaring method for computing the exponential of a matrix. The error analysis of the scaling and squaring method for the exponential of a matrix is applied to the PIM of the DRE. Based on the error analysis, the criterion for choosing two parameters of the PIM is given. Three kinds of IPIMs for solving the DRE are proposed. The numerical examples show that the IPIM is stable and gives the machine accuracy solutions.