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The computation of spectral representations for evolution PDE: Theory and application - Couverture souple

Vetra-Carvalho, Sanita

 
9783639220247: The computation of spectral representations for evolution PDE: Theory and application
Couverture souple
ISBN 10 : 3639220242 ISBN 13 : 9783639220247
Editeur : VDM Verlag Dr. Müller, 2010

Synopsis

In this book the solution representations obtained from a recently developed Fokas integral method for solving boundary value problems for linear evolution PDEs are evaluate numerically. In particular, the case of the linear KdV equation is considered. The Fokas method is quite general and it is therefore of wider interest to assess its competitiveness for numerical purposes. Until now pseudospectral methods have been know to be the most accurate numerical scheme for smooth functions. To compare the two methods, the linear KdV equation is computed numerically using both, a pseudospectral method and the direct evaluation of the integral representation. The two methods are compared for accuracy and speed of the numerical computation, showing that for linear evolutionary PDEs the numerical implementation of Fokas method is much faster and more accurate than a pseudospectral method. The nonlinear KdV equation is also looked at using pseudospectral methods and a motivation for a possible hybrid method which would use both the Fokas and pseudospectral methods together is given.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Présentation de l'éditeur

In this book the solution representations obtained from a recently developed Fokas integral method for solving boundary value problems for linear evolution PDEs are evaluate numerically. In particular, the case of the linear KdV equation is considered. The Fokas method is quite general and it is therefore of wider interest to assess its competitiveness for numerical purposes. Until now pseudospectral methods have been know to be the most accurate numerical scheme for smooth functions. To compare the two methods, the linear KdV equation is computed numerically using both, a pseudospectral method and the direct evaluation of the integral representation. The two methods are compared for accuracy and speed of the numerical computation, showing that for linear evolutionary PDEs the numerical implementation of Fokas method is much faster and more accurate than a pseudospectral method. The nonlinear KdV equation is also looked at using pseudospectral methods and a motivation for a possible hybrid method which would use both the Fokas and pseudospectral methods together is given.

Biographie de l'auteur

Originally from Latvia, I have obtained BSc in computational mathematics (2006) from University of Reading and MSc in mathematics (2007). Currently I am a PhD student at University of Reading holding a grant from NERC and Met Office (to be completed in 2011).

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
VDM Verlag Dr. Müller
Date d'édition
2010
Langue
anglais
ISBN 10 
3639220242
ISBN 13 
9783639220247
Reliure
Broché
Nombre de pages
68
Coordonnées du fabricant
non disponible
Personne responsable
non disponible