A combinational efficient algorithm for elliptic eigenvalue problems. Issue 2 (June 2016) - Zhang, Huirong; Cao, Jianwen
In this paper, we present a combinational efficient algorithm for solving second-order elliptic ordinary differential equation eigenvalue problems on four kinds of meshes. Firstly, a combinational scheme is proposed by leveraging the linear finite element scheme and the second-order finite difference scheme based on mass lumping method. An efficient algorithm is constructed by using the combinational scheme with a constant combined parameter. Then, we improve the efficient algorithm by computing the quasi-optimal combined parameters for different eigenvalues. Finally, numerical experiments tested on both uniform and nonuniform meshes are shown to illustrate the efficiency of our algorithms.