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

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by Maurizio Falcone and Roberto Ferretti


2014 / xii + 319 pages / Softcover / ISBN: 978-1-611973-04-4 / List Price $105.50 / SIAM Member Price $73.85 / Order Code OT133

Keywords: numerical analysis, Hamilton–Jacobi equations, semi-Lagrangian schemes, control theory, geophysical sciences, image processing


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.

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.

About the Authors
Maurizio Falcone is 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 has been an invited professor at ENSTA (Paris), the IMA (Minneapolis), Paris 6 and 7, PIMS (Vancouver and Banff), the Russian Academy of Sciences (Moscow), and UCLA and has coordinated international research projects with France, Russia, and the European Community (Marie Curie). 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 Associate Professor in Numerical Analysis at Roma Tre University. He has spent invited research periods at UCLA, IHP Paris, Goroda Pereslavlya University (Pereslavl-Zalessky, Russia),Technical University of Madrid, ENPC Paris, and ENSTA Paris. He is the author of about 35 research papers in international journals and in proceedings, most of which are on semi-Lagrangian schemes. His main research areas are numerical analysis, PDEs, control theory, image processing, and environmental fluid dynamics.

ISBN: 9781611973044

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