Analytical solution of nonlinear second-order periodic boundary value problem using reproducing kernel method

作者：Shawagfeh Nabil; Abu Arqub Omar; Momani Shaher^*

来源：Journal of Computational Analysis and Applications, 2014, 16(4): 750-762.

• periodic boundary value problems
• Reproducing kernel Hilbert space method

This paper investigates the numerical solution of nonlinear second-order periodic boundary value problems by using reproducing kernel Hilbert space method. The solution was calculated in the form of a convergent series in the space W with easily computable components. In the proposed method, the n-term approximation is obtained and is proved to converge to the analytical solution. Meanwhile, the error of the approximate solution is monotone decreasing in the sense of the norm of W. The proposed technique is applied to several examples to illustrate the accuracy, efficiency, and applicability of the method. The results reveal that the method is very effective, straightforward, and simple.

• 出版日期2014-5