Constructive approximation of solution for fourth-order nonlinear boundary value problems

摘要

In this paper, we obtain a sequence of approximate solution converging uniformly to the exact solution of a class of fourth-order nonlinear boundary value problems. Its exact solution is represented in the form of series in the reproducing kernel space. The n-term approximation u(n)(x) is proved to converge to the exact solution u(x). Moreover, the derivatives of u(n)(x) are also convergent to the derivatives of u(x).