Existence, Uniqueness and Fourth-Order Numerical Method for Solving Fully Third-Order Nonlinear ODE with Integral Boundary Conditions (Journal of Nonlinear Modeling and Analysis, 2025)
In this paper, we establish the existence, uniqueness and constructfourth-order numerical method for solving fully third-order nonlinear differential equation with integral boundary conditions. The method is based on thediscretization of an iterative method on continuous level with the use of thetrapezoidal quadrature formulas with corrections. Some examples demonstratethe applicability of the theoretical results of existence and uniqueness of solution and the fourth-order convergence of the proposed numerical method. Theapproach used for the third-order nonlinear differential equation with integralboundary conditions can be applied to differential equations of any order.