A computational linear stability analysis of spiral waves in a reaction-diffusion equation is performed on large disks. As the disk radius R increases, eigenvalue spectra converge to the absolute spectrum predicted by Sandstede and Scheel. The convergence rate is consistent with 1/R, except possibly near the edge of the spectrum. Eigenfunctions computed on large disks are compared with predicte...

Abstract We study the eigenvalues and eigenfunctions of one-dimensional weighted fractal Laplacians. These Laplacians are defined by self-similar measures with overlaps. first prove existence eigenfunctions. then set up a framework for to discretize equation defining eigenfunctions, obtain numerical approximations eigenvalue eigenfunction using finite element method. Finally, we show that conve...

We report a numerical study of the flexural modes of a plate using semi-classical analysis developed in the context of quantum systems. We first introduce the Clover billiard as a paradigm for a system inside which rays exhibit stable and chaotic trajectories. The resulting phase space explored by the ray trajectories is illustrated using the Poincare surface of section, and shows that it has b...

‎this paper considers a non-local initial-boundary value problem containing a first order partial differential equation with variable coefficients‎. ‎at first‎, ‎the non-self-adjoint spectral problem is derived‎. ‎then its adjoint problem is calculated‎. ‎after that‎, ‎for the adjoint problem the associated eigenvalues and the subsequent eigenfunctions are determined‎. ‎finally the convergence ...

The class of differential-equation eigenvalue problems −y′′(x)+x2N+2y(x) = xNEy(x) (N = −1, 0, 1, 2, 3, . . .) on the interval −∞ < x < ∞ can be solved in closed form for all the eigenvalues E and the corresponding eigenfunctions y(x). The eigenvalues are all integers and the eigenfunctions are all confluent hypergeometric functions. The eigenfunctions can be rewritten as products of polynomial...

Abstract In this work, we consider a boundary value problem for q -Dirac equation. We prove orthogonality of the eigenfunctions, realness eigenvalues, and study asymptotic formulas eigenfunctions. show that eigenfunctions form complete system, obtain expansion formula with respect to derive Parseval’s equality. construct Weyl solution function. uniqueness theorem inverse

Essential information about the stationary and slow kinetic properties of macromolecules is contained in the eigenvalues and eigenfunctions of the dynamical operator of the molecular dynamics. A recent variational formulation allows to optimally approximate these eigenvalues and eigenfunctions when a basis set for the eigenfunctions is provided. In this study, we propose that a suitable choice ...