Solving a class of linear nonlocal boundary value problems using the reproducing kernel

Abstract

Recently, the reproducing kernel Hilbert space methods(RKHSM) (see Wang et al (2011) [2]; Lin and Lin (2010) [3]; Wu and Li (2011) [4]; Zhou et al. (2009) [6]; Jiang and Chen (2014) [7]; Wang et al. (2010) [8]; Du and Cui (2008) [9]; Akram et al. (2013) [10]; Lü and Cui (2010) [11]; Wang et al. (2008) [12]; Yao and Lin (2009) [13]; Geng et al. (2014) [14] ; Arqub et al. (2013) [15]) emerged one after the other. But, a lot of difficult work should be done to deal with multi-point boundary value problems(BVPs). Our work is aimed at giving a new reproducing kernel method for multi-point BVPs. We do not put the homogenization conditions into the reproducing kernel space which can avoid to compute the reproducing kernel satisfying boundary conditions and the orthogonal system. Three numerical examples are studied to demonstrate the accuracy of the present method. Results obtained by our method indicate that new algorithm has the following advantages: small computational work, fast convergence speed and high precision.