Configuration Impulsive Differential Equations

This paper mainly discusses collocation methods for impulsive diferential equa-tions. This kind of equations have the characteristic of both continuous systems anddiscrete systems, but beyond the scope of these two systems. The developments ofmany practical problems are completed by the instant mutation. The impulsivediferential equations can reflect the change law of things deeply and exactly. Asthe development of science and technology, people have realized the importance andthe value of impulsive diferential equations in practice.Firstly, the domestic and overseas development states of impulsive diferentialare introduced.Secondly, by applying collocation methods to impulsive diferential equations,the general form of collocation solution is obtained, and the theorem of existenceand uniqueness of the collocation solution is given.Thirdly, the global convergence of the collocation solution for impulsive difer-ential equations is studied for m arbitrary collocation parameters.Then, when m collocation parameters are subject to some orthogonality condi-tions, the global and local supconvergence of the collocation solution for impulsivediferential equations is analyzed.In addition, the conditions that the analytic and collocation solutions are asymp-totical stable are obtained, and the conditions that numerical solutions preserve thestability property of the analytic ones are given.At last, the correctness of the conclusions given in this thesis are demonstratedby numerical examples.