Analytical solution of nonlinear second-order periodic boundary value problem using reproducing kernel 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 W³ ₂ 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 W³ ₂ . The proposed technique is applied to several examples to illustrate the accuracy, effciency, and applicability of the method. The results reveal that the method is very effective, straightforward, and simple.