A sixth order kernel functions approach for nonlinear fourth order boundary value problems

In this paper, based on the reproducing kernel functions and iterative technique, a new sixth order iterative numerical scheme is presented for nonlinear fourth order boundary value problems(FOBVPs). Compared with the existing reproducing kernel functions based numerical techniques for boundary value problems, the present approach is implemented by using the reproducing kernel functions of the reproducing kernel Hilbert space with lower regularity. This leads to good stability of the proposed technique. The results of numerical examples also demonstrate that our approach has higher accuracy for nonlinear FOBVPs.