Semi-Lagrangian Approximation Schemes for Linear and Hamilton-Jacobi Equations

Häftad, Engelska, 2013

1 299 kr

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Beskrivning

This largely self-contained book provides a unified framework of semi-Lagrangian strategy for the approximation of hyperbolic PDEs, with a special focus on Hamilton-Jacobi equations. The authors provide a rigorous discussion of the theory of viscosity solutions and the concepts underlying the construction and analysis of difference schemes; they then proceed to high-order semi-Lagrangian schemes and their applications to problems in fluid dynamics, front propagation, optimal control, and image processing. The developments covered in the text and the references come from a wide range of literature.Audience: Semi-Lagrangian Approximation Schemes for Linear and Hamilton-Jacobi Equations is written for advanced undergraduate and graduate courses on numerical methods for PDEs and for researchers and practitioners whose work focuses on numerical analysis and numerical methods for nonlinear hyperbolic PDEs.

Produktinformation

Utgivningsdatum:2013-11-30
Mått:152 x 229 x undefined mm
Vikt:593 g
Format:Häftad
Språk:Engelska
Antal sidor:332
Förlag:Society for Industrial & Applied Mathematics,U.S.
ISBN:9781611973044

Utforska kategorier

Beräkning och matematisk analys inom Naturvetenskap och teknik

Mer om författaren

Maurizio Falcone is a Professor of Numerical Analysis in the Mathematics Department of Sapienza University of Rome. He is an associate editor for the journal Dynamic Games and Applications and was a member of the scientific board of the CASPUR Consortium for Scientific Computing (2002-2012) and on the steering committee of the ESF Network 'Optimization with PDE Constraints' (2008-2012). He is the author of about 60 papers in international journals. His main research areas are numerical analysis, PDEs, control theory and differential games, and image processing. Roberto Ferretti is an Associate Professor in Numerical Analysis at Roma Tre University. He is the author of about 35 research papers in international journals and proceedings, mostly on semi-Lagrangian schemes. His main research areas are numerical analysis, PDEs, control theory, image processing, and environmental fluid dynamics.

Innehållsförteckning

Preface Notation Chapter 1: Models and motivations Chapter 2: Viscosity solutions of first-order PDEs Chapter 3: Elementary building blocks Chapter 4: Convergence theory Chapter 5: First-order approximation schemes Chapter 6: High-order SL approximation schemes Chapter 7: Fluid Dynamics Chapter 8: Control and games Chapter 9: Front propagation Bibliography Index.