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

Vetra-Carvalho, Sanita

Softcover

ISBN 10: 3639220242 ISBN 13: 9783639220247

Publisher: 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.

About this title

About the Author

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).

Edition details

• Publisher: VDM Verlag Dr. Müller
• Publication date: 2010
• Language: English
• ISBN 10: 3639220242
• ISBN 13: 9783639220247
• Binding: Paperback
• Number of pages: 68