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

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.

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.