Asymptotic expansions of one-dimensional second-order Helmholtz equation with rapidly oscillating coefficient

In this paper, we discuss one-dimensional second-order Helmholtz equation with rapidly oscillating coefficient, and present an asymptotic expansion method for the problem, which will play an important role in numerical computation. Of course, the convergence result and its proof will be given. Then, its corresponding finite element algorithm is proposed. Finally, some numerical experiments are given to investigate the asymptotic expansion method and the finite element algorithm.