Bertil Gustafsson

High Order Difference Methods for Time Dependent PDE (eBook, PDF)

• Format: PDF

Produktbeschreibung

This book covers high order finite difference methods for time dependent PDE. It gives an overview of the basic theory and construction principles by using model examples. The book also contains a general presentation of the techniques and results for well-posedness and stability, with inclusion of the three fundamental methods of analysis both for PDE in its original and discretized form: the Fourier transform, the eneregy method and the Laplace transform.

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Produktdetails

• Verlag: Springer Berlin Heidelberg
• Seitenzahl: 334
• Erscheinungstermin: 6. Dezember 2007
• Englisch
• ISBN-13: 9783540749936
• Artikelnr.: 37369072

Inhaltsangabe

When are High Order Methods Effective?.- Well-posedness and Stability.- Order of Accuracy and the Convergence Rate.- Approximation in Space.- Approximation in Time.- Coupled Space-Time Approximations.- Boundary Treatment.- The Box Scheme.- Wave Propagation.- A Problem in Fluid Dynamics.- Nonlinear Problems with Shocks.- to Other Numerical Methods.

Rezensionen

From the reviews: "This book presents the theory and construction principles of high order finite difference methods (FDM) for numerical solving of time dependent partial differential equations. ... Many types of finite difference schemes are completely studied and numerical experiments and graphs are presented. ... The book is written in a clear and comprehensive manner. It is recommended to researchers, PD students and readers interested in effective methods for numerical solving of partial differential equations." (Snezhana Gocheva-Ilieva, Zentralblatt MATH, Vol. 1146, 2008)