Solving inverse scattering problem for a discrete Sturm–Liouville operator with a rapidly decreasing potential one gets reflection coefficients s± and invertible operators I +Hs± , where Hs± is the Hankel operator related to the symbol s±. The Marchenko– Faddeev theorem (in the continuous case) [6] and the Guseinov theorem (in the discrete case) [4], guarantees the uniqueness of solution of the...

If a Sturm-Liouville problem is given in an open interval of the real line then regular boundary value problems can be considered on compact sub-intervals. For these regular problems, all with necessarily discrete spectra, the eigenvalues depend on both the end-points of the compact intervals, and upon the choice of the real separated boundary conditions at these end-points. These eigenvalues a...

In this paper, we present a comparative study of 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 me...

When solving the inverse scattering problem for a discrete Sturm–Liouville operator with a rapidly decreasing potential, one gets reflection coefficients s± and invertible operators I +Hs± , where Hs± is the Hankel operator related to the symbol s±. The Marchenko–Faddeev theorem [8] (in the continuous case, for the discrete case see [4, 6]), guarantees the uniqueness of the solution of the inve...

In the present paper, we are concerned with a fractional wave equation of Sturm–Liouville type in general star graph. We first give several existence, uniqueness and regularity results weak solutions for one-dimensional case using spectral theory; prove existence to quadratic boundary optimal control problem provide characterization via Euler–Lagrange first-order optimality conditions. then inv...

Inverse spectral problems consist in recovering operators from their spectral characteristics. Such problems play an important role in mathematics and have many applications in natural sciences (see, for example, [1 – 6]). In 1988, the inverse nodal problem was posed and solved for Sturm-Liouville problems by J. R. McLaughlin [7], who showed that the knowledge of a dense subset of nodal points ...

We consider a recently discovered representation for the general solution of the Sturm-Liouville equation as a spectral parameter power series (SPPS). The coefficients of the power series are given in terms of a particular solution of the Sturm-Liouville equation with the zero spectral parameter. We show that, among other possible applications, this provides a new and efficient numerical method...

We study conformal mappings from the unit disk to circular-arc quadrilaterals with four right angles. The problem is reduced to a Sturm-Liouville boundary value problem on a real interval, with a nonlinear boundary condition, in which the coefficient functions contain the accessory parameters t, λ of the mapping problem. The parameter λ is designed in such a way that for fixed t, it plays the r...

In this paper, a computational intelligence method is used for the solution of fractional optimal control problems (FOCP)'s with equality and inequality constraints. According to the Ponteryagin minimum principle (PMP) for FOCP with fractional derivative in the Riemann- Liouville sense and by constructing a suitable error function, we define an unconstrained minimization problem. In the optimiz...

In this paper we investigate a Sturm–Liouville eigenvalue problem on time scales. Existence of the eigenvalues and eigenfunctions is proved. Mean square convergent and uniformly convergent expansions in the eigenfunctions are established. AMS subject classification: 34L10.