A symmetric finite difference method for computing eigenvalues of Sturm-Liouville problems

Homotopy Analysis Method for Computing Eigenvalues of Sturm-Liouville Problems

In this paper, we apply homotopy analysis method (HAM) for computing the eigenvalues of SturmLiouville problems. The parameter h, in this method, helps us to adjust and control the convergence region. The results show that this method has validity and high accuracy with less iteration number in compare to Variation Iteration Method (VIM) and Adomian decomposition method (ADM). Moreover it is il...

Computing Eigenvalues of Singular Sturm-Liouville Problems

We describe a new algorithm to compute the eigenvalues of singular Sturm-Liouville problems with separated self-adjoint boundary conditions for both the limit-circle nonoscillatory and oscillatory cases. Also described is a numerical code implementing this algorithm and how it compares with SLEIGN. The latter is the only effective general purpose software available for the computation of the ei...

computing the eigenvalues of fourth order sturm-liouville problems with lie group method

‎in this paper, we formulate the fourth order sturm-liouville problem (fslp) as a lie group matrix differential equation. by solving this ma- trix differential equation by lie group magnus expansion, we compute the eigenvalues of the fslp. the magnus expansion is an infinite series of multiple integrals of lie brackets. the approximation is, in fact, the truncation of magnus expansion and a gauss...

Dependence of eigenvalues of Sturm-Liouville problems

The eigenvalues of Sturm-Liouville (SL) problems depend not only continuously but smoothly on boundary points. The derivative of the nth eigenvalue as a function of an endpoint satisfies a first order differential equation. This for arbitrary (separated or coupled) self-adjoint regular boundary conditions. In addition, as the length of the interval shrinks to zero all higher eigenvalues march o...

Inequalities among eigenvalues of Sturm-Liouville problems