Numerical Solutions of Partial Differential Equations

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Beschreibung

This book presents some of the latest developments in numerical analysis and scientific computing. Specifically, it covers central schemes, error estimates for discontinuous Galerkin methods, and the use of wavelets in scientific computing.


This book contains an expanded and smoothed version of lecture notes delivered by the authors at the Advanced School on Numerical Solutions of Partial Di?- ential Equations: New Trends and Applications, which took place at the Centre de Recerca Matem` atica (CRM) in Bellaterra (Barcelona) from November 15th to 22nd, 2007. The book has three parts. The ?rst part, by Silvia Bertoluzza and Silvia Falletta, is devoted to the use of wavelets to derive some new approaches in the numerical solution of PDEs, showing in particular how the possibility of wr- ing equivalent norms for the scale of Besov spaces allows to write down some new methods.Thesecondpart,byGiovanniRusso,providesanoverviewofthemodern finite-volume and finite-difference shock-capturing schemes for systems of cons- vationandbalancelaws,with emphasisingiving auni?ed viewofsuchschemesby identifying the essential aspects of their construction. In the last part Chi-Wang Shugivesageneralintroductionto thediscontinuousGalerkinmethods forsolving some classes of PDEs, discussing cell entropy inequalities, nonlinear stability and error estimates. The school that originated these notes was born with the objective of p- viding an opportunity for PhD students, recent PhD doctorates and researchers in general in ?elds of applied mathematics and engineering to catch up with - portant developments in the ?elds and/or to get in touch with state-of-the-art numerical techniques that are not covered in usual courses at graduate level.

From the reviews:

It includes an extended version of the lectures given by the four authors at the Advanced School on Numerical Solutions of Partial Differential Equations: New Trends and Applications, held at the CRM Barcelona between November 15 22, 2007. The book is addressed to masterands, for PhD candidates and to research workers in the fields of applied mathematics and engineering. (Constantin I. Popovici, IASI Polytechnic Magazine, Vol. 22 (1/4), March-December, 2010)

The book is well written and organized at a difficulty level that precisely meets the target audiences' needs. PhD students as well as engineers and researchers in the field of applied mathematics or scientific computing and interested graduate students will find this book an excellent resource to rapid introduction into the field of modern numerical methods . serve as a textbook for graduate level courses in numerical methods . be useful for experienced researchers and practitioners both from academia or industry. (Andrzej Myliski, Control and Cybernetics, Vol. 39 (3), 2010)

Klappentext

This volume offers researchers the opportunity to catch up with important developments in the field of numerical analysis and scientific computing and to get in touch with state-of-the-art numerical techniques.

The book has three parts. The first one is devoted to the use of wavelets to derive some new approaches in the numerical solution of PDEs, showing in particular how the possibility of writing equivalent norms for the scale of Besov spaces allows to develop some new methods. The second part provides an overview of the modern finite-volume and finite-difference shock-capturing schemes for systems of conservation and balance laws, with emphasis on providing a unified view of such schemes by identifying the essential aspects of their construction. In the last part a general introduction is given to the discontinuous Galerkin methods for solving some classes of PDEs, discussing cell entropy inequalities, nonlinear stability and error estimates.



Inhalt
Wavelets and Partial Differential Equations.- What is a Wavelet?.- The Fundamental Property of Wavelets.- Wavelets for Partial Differential Equations.- High-Order Shock-Capturing Schemes for Balance Laws.- Upwind Scheme for Systems.- The Numerical Flux Function.- Nonlinear Reconstruction and High-Order Schemes.- Central Schemes.- Systems with Stiff Source.- Discontinuous Galerkin Methods: General Approach and Stability.- Time Discretization.- Discontinuous Galerkin Method for Conservation Laws.- Discontinuous Galerkin Method for Convection-Diffusion Equations.- Discontinuous Galerkin Method for PDEs Containing Higher-Order Spatial Derivatives.

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Produktinformationen

Titel
Numerical Solutions of Partial Differential Equations
Autor
Schöpfer
EAN
9783764389390
ISBN
978-3-7643-8939-0
Format
Kartonierter Einband
Genre
Mathematik
Anzahl Seiten
202
Gewicht
369g
Größe
H11mm x B240mm x T170mm
Jahr
2008
Untertitel
Englisch
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