Niu, Jing; Xue, Qing; Ran, Cuiping; Liu, Jia; Pan, Haijing Efficient numerical algorithm for approximate solution of the third-order differential equation with boundary value problems. (Chinese. English summary) Zbl 1413.65283 Math. Pract. Theory 47, No. 9, 177-181 (2017). Summary: In this paper, we present an efficient numerical algorithm to solve the third-order system of boundary value problems based on the reproducing kernel Hilbert space method. Using reproducing property and the existence of orthogonal basis in the reproducing kernel Hilbert space, we obtain a representation of exact solution with the form of series and its approximate solution by truncating the series. Moreover, the effectiveness of the presented method is illustrated with two numerical examples. MSC: 65L10 Numerical solution of boundary value problems involving ordinary differential equations Keywords:approximate solution; reproducing kernel Hilbert space; numerical algorithm; linear operator PDFBibTeX XMLCite \textit{J. Niu} et al., Math. Pract. Theory 47, No. 9, 177--181 (2017; Zbl 1413.65283)