5 edition of **Implementing Spectral Methods for Partial Differential Equations** found in the catalog.

- 259 Want to read
- 40 Currently reading

Published
**2009**
by Springer Netherlands in Dordrecht
.

Written in English

- Partial Differential equations,
- Mathematical physics,
- Computer science,
- Mathematics,
- Electronic data processing,
- Physics

**Edition Notes**

Statement | by David A. Kopriva ; edited by J.-J. Chattot, P. Colella, W. Eist, R. Glowinski, Y. Hussaini, P. Joly, H.B. Keller, J.E. Marsden, D.I. Meiron, O. Pironneau, A. Quarteroni, J. Rappaz, R. Rosner, P. Sagaut, J.H. Seinfeld, A. Szepessy, M.F. Wheeler |

Series | Scientific Computation |

Contributions | Marsden, J.E., Quarteroni, A., Rappaz, J., Rosner, R., Sagaut, P., Seinfeld, J.H., Szepessy, A., Wheeler, M.F., Meiron, D.I., Keller, H.B., Hussaini, Y., Eist, W., Glowinski, R., Chattot, J. J., Joly, Pascal, Colella, P., Pironneau, O., SpringerLink (Online service) |

The Physical Object | |
---|---|

Format | [electronic resource] : |

ID Numbers | |

Open Library | OL25542746M |

ISBN 10 | 9789048122608, 9789048122615 |

This book presents applications of spectral methods to problems of uncertainty propagation and quantification in model-based computations, focusing on the computational and algorithmic features of these methods most useful in dealing with models based on partial differential equations, in particular models arising in simulations of fluid flows. 4. Quasi -linearisation Method 5. Spectral Quasi -Linearization 6. Chebyshev Spectral Collocation method (CSCM) 7. Solving Linear and Non -linear Boundary Value problems using the CSCM 8. Solving systems of coupled nonlinear ODEs using SQLM 9. Pseudo -spectral methods for Partial Differential Equations Application in real -life problems.

Spectral methods are a class of techniques used in applied mathematics and scientific computing to numerically solve certain differential equations, potentially involving the use of the fast Fourier transform. spectral methods for partial differential equations in irregular domains: the spectral smoothed boundary method * alfonso buenq'orqviot victor m. perez-garcia * h. fentqn§ abstract. Hi tnis paper, wc> proposea numerical mettioa to approximate Trie solution or partial differential equations in irregular domains with no-flux boundary.

() A high-order embedded domain method combining a Predictor–Corrector-Fourier-Continuation-Gram method with an integral Fourier pseudospectral collocation method for solving linear partial differential equations in complex by: The use of the spectral method in both temporal and spatial discretizations of fractional partial differential equations may significantly reduce the storage requirement because, as compared to low order methods, much fewer time and space Cited by:

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This book offers a systematic and self-contained approach to solve partial differential equations numerically using single and multidomain spectral methods. It contains detailed algorithms in pseudocode for the application of spectral approximations to both one and two dimensional PDEs of mathematical physics describing potentials, transport, and wave Cited by: This book offers a systematic and self-contained approach to solve partial differential equations numerically using single and multidomain spectral methods.

It contains detailed algorithms in pseudocode for the application of spectral approximations to both one and two dimensional PDEs of mathematical physics describing potentials, transport, and wave Brand: Springer Netherlands.

Implementing Spectral Methods for Partial Differential Equations: Algorithms for Scientists and Engineers (Scientific Computation) edition by Kopriva, David A.

() Hardcover [Kopriva, David A.] on *FREE* shipping on qualifying offers. Implementing Spectral Methods for Partial Differential Equations: Algorithms for Scientists and 5/5(1).

The book addresses computationaland applications scientists, as it emphasizes thepractical derivation and implementation of spectral methods over abstract mathematics. It is divided into two parts: First comes a primer on spectralapproximation and the basic algorithms, including FFT algorithms, Gaussquadrature algorithms, and how to approximate.

Implementing Spectral Methods for Partial Differential Equations: Algorithms for Scientists and Engineers. This book explains how to solve partial differential equations numerically using single and multidomain spectral methods.5/5(1).

This book offers a systematic and self-contained approach to solvepartial differential equations numerically using Implementing Spectral Methods for Partial Differential Equations book and multidomain spectralmethods. It contains detailed algorithms in pseudocode for the applicationof spectral approximations to both one and two dimensional PDEsof mathematical physics describing potentials,transport, and Cited by: The fundamental idea behind spectral methods is to approximate solutions of PDEs by finite series of orthogonal functions such as the complex exponentials, Chebyshev, or Legendre polynomials.

Chapter 1 reviews how to approximate functions, derivatives and integrals for both periodic and non-periodic problems using these series. These Proceedings of the first Chinese Conference on Numerical Methods for Partial Differential Equations covers topics such as difference methods, finite element methods, spectral methods, splitting methods, parallel algorithm etc., their theoretical foundation and applications to engineering.

Along with finite differences and finite elements, spectral methods are one of the three main methodologies for solving partial differential equations on computers. This book provides a detailed presentation of basic spectral algorithms, as well as a systematical presentation of basic convergence theory.

The GAMM Committee for "Efficient Numerical Methods for Partial Differential Equations" organizes seminars and workshops on subjects concerning the algorithmic treatment of partial differential equations.

The topics are discretisation methods like the finite element and the boundary element method. From the Back Cover. This book offers a systematic and self-contained approach to solve partial differential equations numerically using single and multidomain spectral methods.

It contains detailed algorithms in pseudocode for the application of spectral approximations to both one and two dimensional PDEs of mathematical physics describing Reviews: 1. This is a book about spectral methods for partial differential equations: when to use them, how to implement them, and what can be learned from their of spectral methods has evolved rigorous theory.

The computational side vigorously since the early s, especially in computationally intensive of the more spectacular applications are. This book explains how to solve partial differential equations numerically using single and multidomain spectral methods.

It shows how only a few fundamental algorithms form the building blocks of any spectral code, even for problems with complex geometries.

Spectral methods are approximation techniques for the computation of the solutions to ordinary and partial differential equations. They are based on a polynomial expansion of the solution. The precision of these methods is limited only by the regularity of the solution, in contrast to the finite difference method and the finite element methods.

About this book. Introduction. Along with finite differences and finite elements, spectral methods are one of the three main methodologies for solving partial differential equations on. Abstract. The representation of spatial derivatives is at the heart of spectral methods for partial differential equations, so the three main kinds (Fourier, Chebyshev and Legendre) are analyzed at the outset, together with efficient means to compute : Simon Širca, Martin Horvat.

plntn ptrl thd fr Prtl Dffrntl tn lrth fr ntt nd nnr 42 Sprnr. ntnt rf rt I Apprxtn ntn, rvtv nd Intrl 1 Sptrl Apprxtn v 3. Prbl: r ltn f PD Th Frr B Fntn nd Frr r 4. r Trntn dl v. Ndl pprxtn 1 I.

Drt rthnlt nd drtr Frr ntrpltn Drt pttn f th Frr ntrpltn the performance and limitations of spectral methods, contains an exhaustive bibliography for spectral methods at the level of year A more strange feature of spectral methods is the fact that, in some sit-uations, they transform self-adjoint diﬀerential problems into non symmetric, i.e., non normal, discrete algebraic Size: 3MB.

Find helpful customer reviews and review ratings for Implementing Spectral Methods for Partial Differential Equations: Algorithms for Scientists and Engineers (Scientific Computation) at Read honest and unbiased product reviews from our users.5/5.

During that decade spectral methods appeared to be well-suited only for problems governed by ordinary diSerential eqllations or by partial differential equations with. This page textbook was written during and used in graduate courses at MIT and Cornell on the numerical solution of partial differential equations.

The book has not been completed, though half of it got expanded into Spectral Methods in MATLAB.A new collocation method for the numerical solution of partial differential equations is presented. This method uses the Chebyshev collocation points, but, because of the way the boundary conditions are implemented, it has all the advantages of the Legendre by: The ultraspherical spectral method was extended to automatically solve general linear partial differential equations on rectangles [66] and the ideas used to do this successfully may well.