An algorithm is presented for computing eigenvalues of regular selfadjoint Sturm-Liouville (SL) problems with matrix coefficients and separated boundary conditions.

We develop spectral element methods for a timeand space-fractional advection equation of the form 0Dt u(x, t) + θ 0Dxu(x, t) = f(x, t), of order τ ∈ (0, 1], ν ∈ (0, 1), subject to Dirichlet initial/boundary conditions. We present two spectrally accurate and efficient methods for global discretization of both temporal and spatial terms, instead of employing traditional low-order time-integration...

We consider compactly supported perturbations of periodic Sturm-Liouville equations. In this context, one can use the Floquet solutions of the periodic background to define scattering coefficients. We prove that if the reflection coefficient is identically zero, then the operators corresponding to the periodic and perturbed equations, respectively, are unitarily equivalent. In some appendices, ...

This paper proposes that the study of Sturm sequences is invaluable in the numerical computation and theoretical derivation of eigenvalue distributions of random matrix ensembles. We first explore the use of Sturm sequences to efficiently compute histograms of eigenvalues for symmetric tridiagonal matrices and apply these ideas to random matrix ensembles such as the β-Hermite ensemble. Using ou...

A regularized trace formula of first order for the matrix Sturm-Liouville equation with eigenparameter in the boundary conditions is obtained.

in this manuscript a new method is introduced for solving fractional differential equations. the fractional derivative is described in the caputo sense. the main idea is to use fractional-order legendre wavelets and operational matrix of fractional-order integration. first the fractional-order legendre wavelets (flws) are presented. then a family of piecewise functions is proposed, based on whi...