Computing high-index eigenvalues for the Sturm-Liouville equation with Robin boundary conditions

The calculation of the high-indexed eigenvalues of Sturm-Liouville problems tends to be a complex job. The larger the eigenvalues are estimated, the greater the scaled errors we gain. In this paper, we study the Sturm-Liouville problems subject to Rubin boundary conditions in which the high-indexed eigenvalues are computed by means of an efficient method. In contrast to previous methods, the estimated errors of further eigenvalues are less than the primary ones. A good illustration of the accuracy of our method can be delineated by some numerical examples.

کلیدواژه ها:

Sturm-Liouville operator ، Robin boundary condition ، High-index eigenvalue ، Quadrature method