Titlebook: Spectral Methods for Non-Standard Eigenvalue Problems; Fluid and Structural Călin-Ioan Gheorghiu Book 2014 The Author(s) 2014 Galerkin spec

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The Chebyshev Collocation Method,genvalue problem. A special attention is paid to the well known Mathieu’s system as a MEP. A lot of eigenmodes and eigenfrequencies corresponding to various geometries of the vibrating elliptic membrane problem, in which this system is originated, are displayed. In order to avoid spurious eigenvalue

空中

The Laguerre Collocation Method,ered. A special attention is payed to the influence of the scaling parameter (which maps the half-line into itself) on the repartition of the Laguerre nodes. We manually tune this geometrical parameter in order resolve narrow regions with high variations of solutions, i.e., the so called boundary or

majestic

松驰

放纵

注意到

Tau and Galerkin Methods for Fourth Order GEPs,of these problems are self-adjoint a weak (variational) along with a minimization formulation are suggested. The Galerkin method is analyzed with respect to the possibility to choice test and trial functions in order to improve the properties of the differentiation (discretization) matrices, i.e., c

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Militia

The Laguerre Collocation Method, of these functions is the fact that they decrease smoothly to zero at infinity along with their derivatives. We speculate this behavior in imposing boundary conditions at large distances. On the half-line we solve high order eigenvalue problems, linear as well as some genuinely nonlinear third and

LAPSE

Conclusions and Further Developments,ation on an unbounded domain is based on Laguerre functions. Practical and computational aspects of these methods are mainly emphasized. High order eigenvalue problems, i.e., of fourth, sixth and eighth orders along with genuinely nonlinear and singular perturbed two-point eigenvalue problems are co