For a system of coupled Schrödinger equations, the relationship is found between the vector-valued norming constants and M + 1 spectra of the M-channel Sturm-Liouville operator with the same potential matrix but different boundary conditions. Under a special choice of particular boundary conditions, this equation for norming vectors has a unique solution. The norming vectors derived from M + 1 ...

We study the complexity of approximating the smallest eigenvalue of a univariate Sturm-Liouville problem on a quantum computer. This general problem includes the special case of solving a one-dimensional Schrödinger equation with a given potential for the ground state energy. The Sturm-Liouville problem depends on a function q, which, in the case of the Schrödinger equation, can be identified w...

This paper gives the analysis and numerics underlying a shooting method for approximating the eigenvalues of nonselfadjoint Sturm-Liouville problems. We consider even order problems with (equally divided) separated boundary conditions. The method can nd the eigenvalues in a rectangle and in a left half-plane. It combines the argument principle with the compound matrix method (using the Magnus e...

The method proposed here has been devised for solution of the spectral problem for the Lamé wave equation (see [2]), but extended lately to more general problems. This method is based on the phase function concept or the Prüfer angle determined by the Prüfer transformation cot θ(x) = y′(x)/y(x), where y(x) is a solution of a second order self-adjoint o.d.e. The Prüfer angle θ(x) has some useful...

where λ is a spectral parameter, Y (x) = [yk(x)]k=1,d is a column vector, Q(x) and M(x, t) are d×d real symmetric matrix-valued functions, and h and H are d×d real symmetric constant matrices. M(x, t) is an integrable function on the set D0 def ={(x, t) : 0≤ t ≤ x ≤ π, x, t ∈ R}, Q ∈ C1[0,π], where C1[0,π] denotes a set whose element is a continuously differentiable function on [0,π]. In partic...

Abstract The Sturm–Liouville differential equation is one of interesting problems which has been studied by researchers during recent decades. We study the existence a solution for partial fractional using α - ψ -contractive mappings. Also, we give an illustrative example. By -multifunctions, prove solutions inclusion version problem. Finally providing another example and some figures, try to i...

This paper considers the problem of viscous dissipation in the flow of Newtonian fluid through a tube of annular cross section, with Dirichlet boundary conditions. The solution of the problem is obtained by a series expansion about the complete eigenfunctions system of a Sturm-Liouville problem. Eigenfunctions and eigenvalues of this Sturm-Liouville problem are obtained by Galerkin’s method.

Under additional conditions uniqueness of the solution is proved for the following problem. Given 1) the spectrum of the Dirichlet problem for the Sturm–Liouville equation on [0, a] with real potential q(x) ∈ L2(0, a), 2) a certain part of the spectrum of the Dirichlet problem for the same equation on [ 3 , a] and 3) the potential on [0, a 3 ]. The aim is to find the potential on [ 3 , a].

Recently a great deal of interest has been focused on the application of HPM for the solution of many different problems. The technique has been applied with great success to obtain the solution of a large variety of nonlinear problems in both ordinary and partial differential equations and integro-differential equations[1-10]. In this work we apply HPM to approximate eigenvalues and eigenfunct...

In this paper, we study the non-definite Sturm-Liouville problem comprising of a regular Sturm-Liouville equation and Dirichlet boundary conditions on a closed interval. We consider the case in which the weight function changes sign twice in the given interval of definition. We give detailed numerical results on the spectrum of the problem, from which we verify various results on general non de...