Convergence Of Solutions For Several Types Differential Equations With Initial Value Problems

In this paper,the convergence of solutions for several types differential equations are investigated,by using quasilinearization method and interval analysis.The main content of this paper includes the following three parts.In part one,The quasilinearization method,AscoliArzela theory and Gronwall's inequality are applied to discuss the convergence of the solutions for a class of second-order functional differential equations with initial condition,we obtain the conditions of quadratic convergence of the approximate solutions.In part two,we employ the generalized quasilinearization for initial value problems of set functional equations to weaken the concave-convex restrictions on the function F,then obtain monotone sequences which converge uniformly quadratically to the unique solution of the problem.In part three,we consider the initial value problems of first order differential equations by combining the interval analysis and quasilinearization,and the sequences of interval functions converging uniformly and higher order convergence to a solution of the problem are obtained.