Applied Mathematics Letters ( IF 3.848 ) Pub Date : 2020-09-12 , DOI: 10.1016/j.aml.2020.106732 Hongbo Sun; Liangcai Mei; Yingzhen Lin
In this article, a new algorithm based on improved Legendre orthonormal basis for solving second-order BVPs is constructed. The method of this article is an improved Legendre orthogonal polynomial algorithm, and the -best approximate solution is constructed skillfully in the reproducing kernel space. Compared with other methods, this method has the advantages of high approximation, -order convergence and strong stability. Some numerical examples show the effectiveness and stability of the algorithm.