Existence, Uniqueness and Fourth-Order Numerical Method for Solving Fully Third-Order Nonlinear ODE with Integral Boundary Conditions

Abstract

In this paper, we establish the existence, uniqueness and construct fourth-order numerical method for solving fully third-order nonlinear differential equation with integral boundary conditions. The method is based on the discretization of an iterative method on continuous level with the use of the trapezoidal quadrature formulas with corrections. Some examples demonstrate the applicability of the theoretical results of existence and uniqueness of solution and the fourth-order convergence of the proposed numerical method. The approach used for the third-order nonlinear differential equation with integral boundary conditions can be applied to differential equations of any order.