An introduction to spectral methods for partial differential equations. (English) Zbl 0731.65073
Advances in numerical analysis. Vol. I: Nonlinear partial differential equations and dynamical systems, Proc. 4th Summer Sch., Lancaster/UK 1990, 96-146 (1991).
[For the entire collection see Zbl 0724.00022.]
An elementary introduction to spectral methods for the numerical solution of boundary value problems is presented. The properties of Fourier and Chebyshev spectral approximations are revisited. The spectral collocation method is applied to elliptic boundary value problems, advection- diffusion equations and Navier-Stokes equations. Finally domain decomposition techniques which allow the applicability of spectral methods to problems in complex geometries are discussed. Hereby it becomes clear how to match effectively the features of multiprocessor systems.
An elementary introduction to spectral methods for the numerical solution of boundary value problems is presented. The properties of Fourier and Chebyshev spectral approximations are revisited. The spectral collocation method is applied to elliptic boundary value problems, advection- diffusion equations and Navier-Stokes equations. Finally domain decomposition techniques which allow the applicability of spectral methods to problems in complex geometries are discussed. Hereby it becomes clear how to match effectively the features of multiprocessor systems.
Reviewer: W.Heinrichs (Düsseldorf)
MSC:
| 65L60 | Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations |
| 65L10 | Numerical solution of boundary value problems involving ordinary differential equations |
| 65N35 | Spectral, collocation and related methods for boundary value problems involving PDEs |
| 65N55 | Multigrid methods; domain decomposition for boundary value problems involving PDEs |
| 34B05 | Linear boundary value problems for ordinary differential equations |
| 35J25 | Boundary value problems for second-order elliptic equations |
