Approximations of Sturm-Liouville eigenvalues using Sinc-Galerkin and differential transform methods

Abstract:
In recent years there has been a considerable renewal of interest in the Sturm-Liouville eigenvalue problem, from point of view of both mathematics and their applications to physics and engineering. For many important applications in science and engineering it is required to determine the eigenvalues as well as the corresponding eigenfunctions. In application, for instance, involving vibration and stability of deformable bodies, the viral piece of information required is the smallest eigenvalue. In this paper, we present a comparative study between Sinc-Galerkin method and differential transform method to solve Sturm-Liouville eigenvalue problem. As an application, a comparison between the two methods for various celebrated Sturm-Liouville problems are analyzed for their eigenvalues and solutions. The study outlines the significant features of the two methods. The results show that these methods are very efficient, convenient and can be applied to a large class of problems. The comparison of the methods shows that although the numerical results of these methods are the same, differential transform method is much easier, more convenient and efficient than the Sinc-Galerkin method.