Abstract. We present a new numerical method for computing the pure-point spectrum associated with the linear stability of coherent structures. In the context of the Evans function shooting and matching approach, all the relevant information is carried by the flow projected onto the underlying Grassmann manifold. We show how to numerically construct this projected flow in a stable and robust manner. In particular, the method avoids representation singularities by, in practice, choosing the best coordinate patch representation for the flow as it evolves. The method is analytic in the spectral parameter and of complexity bounded by the order of the spectral problem cubed. For large systems it represents a competitive method to those recently developed that are based on continuous orthogonalization. We demonstrate this by comparing the two methods in three applications: Boussinesq solitary waves, autocatalytic travelling waves and the Ekman boundary layer.
Abstract. The main purpose of this paper is to describe the extension of the successful modified integral series methods for Schrödinger problems to more general Sturm-Liouville eigenvalue problems. We present a robust and reliable modified Neumann method which can handle a wide variety of problems. This modified Neumann method is closely related to the second-order Pruess method, but provides for higher order approximations. We show that the method can be successfully implemented in a competitive automatic general-purpose software package.
MATSLISE is a graphical MATLAB software package for the interactive numerical study of regular Sturm-Liouville problems, one-dimensional Schrödinger equations, and radial Schrödinger equations with a distorted Coulomb potential. It allows the fast and accurate computation of the eigenvalues and the visualization of the corresponding eigenfunctions. This is realized by making use of the power of high-order piecewise constant perturbation methods, a technique described by Ixaru. For a well-outlined class of problems, the implemented algorithms are more efficient than the well-established SL-solvers SL02f, SLEDGE, SLEIGN, and SLEIGN2, which are included by Pryce in the SLDRIVER code that has been built on top of SLTSTPAK.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.