Third Order Convergence for Nonlinear Impulsive Differential Equations with a Nonlinear Three-point Boundary Condition

摘要

The method of generalized quasilinearization has been extended for nonlinear impulsive differential equations with a nonlinear three-point boundary condition. Natural lower and upper solutions under suitable conditions are considered. We have obtained two sequences which converge uniformly and monotonically to the unique solution of the nonlinear impulsive differential equations. We further prove that the rate of convergence is cubic.