In this paper, we give the spectral theory for eigenvalues and eigenfunctions of a boundary value problem consisting of the linear fractional Bessel operator. Moreover, we show that this operator is self-adjoint, the eigenvalues of the problem are real, and the corresponding eigenfunctions are orthogonal. In this paper, we give the spectral theory for eigenvalues and eigenfunctions...

We consider a non-self-adjoint fourth order eigenvalue problem using a discontinuous Galerkin (DG) method. For high order problems, DG methods are competitive since they use simple basis functions and have less degrees of freedom. The numerical implementation is much easier compared with classical finite element methods. In this paper, we propose an interior penalty discontinuous Galerkin metho...

a mathematical model is presented in the present study to control‎ ‎the light propagation in an inhomogeneous media‎. ‎the method is ‎based on the identification of the optimal materials distribution‎ ‎in the media such that the trajectories of light rays follow the‎ ‎desired path‎. ‎the problem is formulated as a distributed parameter ‎identification problem and it is solved by a numerical met...

This work proposes a new adaptive remeshing strategy based on the sensitivity of the point wise error in stresses with respect to the nodal coordinates, which is computed using the adjoint-state method. This sensitivity provides information about the influence of the discretization of each zone of the computational domain in the estimation of the error in stresses at a specific point. This info...

Singularly perturbed boundary value problem can be solved using various techniques. The solution of the following fourth order self adjoint singularly perturbed boundary value problem is approximated using quintic spline Ly = − y(4) + p(x)y = f(x), p(x) ≥ p > 0, y(a) = α0, y(b) = α1, y(1)(a) = α2, y(1)(b) = α3, } or Ly = − y(4) + p(x)y = f(x), p(x) ≥ p > 0, y(a) = α0, y(b) = α1, y(2)(a) = α4, y...

This paper deals with the eigenvalue singular problem of the spectral type differential equations of the fourth-order self-adjoint differential operators 1 ð1 xÞð1þ xÞ d dx ð1 xÞð1þ xÞ d y dx " # ly 1⁄4 0; yð 1Þ; yð1Þ finite where, p P 1; q P 1. It has been reported in the literature that spectral type differential equations above have general solutions in terms of hypergeometric functions. In ...

In applications, many states given for a system can be expressed by orthonormal elements, called “state elements”, taken in separable Hilbert space (called space”). The exact nature of the depends on system; example, state position and momentum is square-integrable functions. symmetries quantum represented class unitary operators that act space. ladder have effect lowering or raising energy sta...