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 u(n)(x) is represented in the reproducing kernel space. It is proved that u(n)(x) converges uniformly to the exact solution u(x). Moreover, the derivatives of u(n)(x) are also convergent to the derivatives of u(x). Numerical results show that the method employed in the paper is valid.