1,720,965 research outputs found
A corrected spectral method for Sturm–Liouville problems with unbounded potential at one endpoint
Full text linkIn this paper, we shall derive a spectral matrix method for the approximation of the eigenvalues of (weakly) regular and singular Sturm–Liouville problems in normal form with an unbounded potential at the left endpoint. The method is obtained by using a Galerkin approach with an approximation of the eigenfunctions given by suitable combinations of Legendre polynomials. We will study the errors in the eigenvalue estimates for problems with unsmooth eigenfunctions in proximity of the left endpoint. The results of this analysis will be then used conveniently to determine low-cost and effective procedures for the computation of corrected numerical eigenvalues. Finally, we shall present and discuss the results of several numerical experiments which confirm the effectiveness of the approach
Test set for initial value problem solvers, release 2.4, http://www.dm.uniba.it/~testset/
No full textA Generalization of Numerov's Method Using the BVM Approach for Sturm-Liouville Eigenvalue estimates
No full textBoundary Value Methods generalizing the Numerov's method are here proposed for the numerical approximation of the eigenvalues of regular Sturm-Liouville problems subject to Dirichlet boundary conditions. Moreover, an analysis of the error in the approximation of the k-th eigenvalue provided by such methods is reported. Some numerical results showing the possible advantages that may arise from the use of the new schemes are also presented
Efficient implementation of Radau collocation methods
No full textIn this paper we define an efficient implementation of Runge-Kutta methods of Radau IIA type, which are commonly used when solving stiff ODE-IVPs problems. The proposed implementation relies on an alternative low-rank formulation of the methods, for which a splitting procedure is easily defined. The linear convergence analysis of this splitting procedure exhibits excellent properties, which are confirmed by its performance on a few numerical tests
Boundary Value Methods for the Reconstruction of Sturm-Liouville potentials
No full textThe paper deals with the numerical solution of the two-spectra and the half inverse Sturm-Liouville problems. The numerical procedure proposed provides a continuous approximation of the unknown potential and uses an approach similar to the one studied in [6] for solving the symmetric inverse problem. The results of numerical experiments confirm the effectiveness of the considered methods
BVMs for Sturm-Liouville eigenvalue estimates with general boundary conditions
No full textRecently, a class of Boundary Value Methods (BVMs) has been introduced for the estimation of the eigenvalues of Sturm-Liouville problems with Dirichlet boundary conditions. The aim of this paper is to extend the application of such BVMs to problems with boundary conditions of general form and to compare the approximations obtained with those given by the corrected Numerov method
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Spectral solution of ODE-IVPs by using SHBVMs
Full text linkRecently, Hamiltonian Boundary Value Methods (HBVMs), have been used as spectral methods in time for effectively solving multi-frequency, highly-oscillatory and/or stiffly-oscillatory problems. A complete analysis of their use in such a fashion has been also carried out, providing a theoretical framework explaining their effectiveness. We report here a few numerical examples showing their potentialities to provide a fully accurate solver for general ODE problems
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