Quasilinearization Of An Initial Value Problem For Set Differential Equations

With the development of science and technology, in the field of science and social science, nonlinear problems are becoming more and more important and it has got more attention. Non-linear problems exist in physics, chemistry and biology, even social and economic problems. Because of seeking general solution for nonlinear set differential equations is difficult, so it would be a meaningful task solving it in theory and the study for set differential equation be-come into a hot topic, The general quasilinearization method and the quasilinearization method are one of the ways to research the solution of converge speeds, but so far, A few of home and abroad learners study the set differential equation convergence.This article is mainly applied general quasilinearization method and quasilinearization method to set differential equations and discusses the solution convergence of different types of set differential equations. In Chapter 1, we give a survey to the development and current state of set differential equations, as well as the main work status of this paper. In Chapter 2 and 3, by using general quasilinearization method and quasilinearization method we study two different types of set differential equations and set integro-differential equations, obtaining two monotone uniformly convergence sequences to the unique solution and the convergence is quadratic. In Chapter 4, we consider the set differential equation on Banach space, obtaining two monotone uniformly convergence sequences to the unique solution and the convergence is suplinear.