The Solution of Nonlinear Fourth-Order Differential Equation with Integral Boundary Conditions

An iterative algorithm is proposed for solving the solution of a nonlinear fourth-order differential equation with integral boundary conditions. Its approximate solution un(x) is represented in the reproducing kernel space. It is proved that un(x) converges uniformly to the exact solution u(x). Moreover, the derivatives of un(x) are also convergent to the derivatives of u(x). Numerical results show that the method employed in the paper is valid