A reproducing kernel Hilbert space method for solving the nonlinear three‐point boundary value problems

Abstract

AbstractThe main objective of this paper is to present a reproducing kernel Hilbert space method for computing solutions of nonlinear third‐order ordinary differential equations under multipoint boundary conditions. Some other aspects of the reproducing kernel Hilbert space method, such as convergence analysis and error estimate, are also discussed. The proposed method is a well‐performance technique for calculating the best approximate solution of nonlinear boundary value problems. Our numerical experiments validate our theoretical findings and demonstrate the desirable performance of the algorithm in terms of simplicity, accuracy, and efficiency.