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Spectral methods for differential problems. (English) Zbl 1122.65118
Cluj-Napoca: Casa Cărţii de Ştiinţă (ISBN 978-973-133-099-0/pbk). x, 154 p. (2007).
This book shows the capabilities of spectral and pseudospectral methods in solving boundary value problems for differential and partial differential equations as well as in solving initial-boundary value problems for parabolic and hyperbolic equations. Both, linear and genuinely nonlinear problems are taken into account. The class of linear boundary value problems include singularly perturbed problems and eigenvalue problems. The book is not oriented on formal reasoning. Instead, it displays the most important qualities as well as drawbacks of spectral methods for boundary value, initial-boundary value and eigenvalue problems for partial differential equations.

65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
65-02 Research exposition (monographs, survey articles) pertaining to numerical analysis
65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
65N25 Numerical methods for eigenvalue problems for boundary value problems involving PDEs
65L15 Numerical solution of eigenvalue problems involving ordinary differential equations