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Spectral collocation solutions to problems on unbounded domains. (English) Zbl 1453.65004

Cluj-Napoca: Casa Cărţii de Ştiinţă (ISBN 978-606-17-1272-4/pbk). xvi, 151 p. (2018).
A usual procedure in discretizing problems on unbounded domains is to cut off an exterior part of the domain, to impose suitable boundary conditions on the newly obtained boundary and then to apply methods designed for problems on bounded domains. The author instead discretizes the problems directly as given by spectral approximation with trial functions defined on the entire domain combined with collocation in a finite number of points. As trial function he considers Hermite functions, Laguerre functions (with both the roots of the Laguerre polynomials and the Gauss-Radau nodes as collocation points) and sinc functions and also a mapping technique. The trial functions depend on a scaling parameter which is also adapted for obtaining good results.
The author concentrates on presenting a large number of numerical results, an analysis of the methods is not in the focus. The book contains 105 figures and 23 tables (a list of problems considered can be found under the above keywords). The calculations are performed using MATLAB (for some representative problems MATLAB scripts are given in the fifth chapter of the book). The bibliography comprises 195 items.
The book is for sale at 19.99 Euro. But I think that this affordable price is not the explanation for the not so successful layout of the figures. They seem to be placed at random in the center, at the left margin, colored or not, with weakly or firmly printed labels and lines.

MSC:

65-02 Research exposition (monographs, survey articles) pertaining to numerical analysis
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
65L15 Numerical solution of eigenvalue problems involving ordinary differential equations
65N15 Error bounds for boundary value problems involving PDEs
65D05 Numerical interpolation
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