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 $\epsilon$-best approximate solution is constructed skillfully in the reproducing kernel space. Compared with other methods, this method has the advantages of high approximation, $m$-order convergence and strong stability. Some numerical examples show the effectiveness and stability of the algorithm.

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