4 research outputs found
NUMERICAL SOLUTION OF PERTURBATION STURM-LIOUVILLE PROBLEMS USING CHEBYSHEV POLYNOMIAL
In this paper, a boundary value problem which consists of the integro-differential equation is considered, Chebyshev polynomial is used to find the numerical solution of perturbation Sturm-Liouville problems, an example of numerical results are given and algorithms are performed by Mathmatica (0.7) program
Sturm Liouville Problem with Moving Discontinuity Points
In this paper, we present a new discontinuous Sturm Liouville problem with
symmetrically located discontinuities which are defined depending on a
neighborhood of a midpoint of the interval. Also the problem contains an
eigenparameter in one of the boundary conditions and has coupled transmission
conditions at the discontinuity points. We investigate the properties of the
eigenvalues, obtain asymptotic formulas for the eigenvalues and the
corresponding eigenfunctions and construct Green's function of this problem.Comment: 19 pages. arXiv admin note: text overlap with arXiv:1210.4350 by
other author
Centrosymmetric Matrices in the Sinc Collocation Method for Sturm-Liouville Problems
Recently, we used the Sinc collocation method with the double exponential
transformation to compute eigenvalues for singular Sturm-Liouville problems. In
this work, we show that the computation complexity of the eigenvalues of such a
differential eigenvalue problem can be considerably reduced when its operator
commutes with the parity operator. In this case, the matrices resulting from
the Sinc collocation method are centrosymmetric. Utilizing well known
properties of centrosymmetric matrices, we transform the problem of solving one
large eigensystem into solving two smaller eigensystems. We show that only
1/(N+1) of all components need to be computed and stored in order to obtain all
eigenvalues, where (2N+1) corresponds to the dimension of the eigensystem. We
applied our result to the Schr\"odinger equation with the anharmonic potential
and the numerical results section clearly illustrates the substantial gain in
efficiency and accuracy when using the proposed algorithm.Comment: 11 pages, 4 figure