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

A self-contained guide to semi-Lagrangian approximation of Hamilton–Jacobi equations and applications to fluid dynamics, optimal control, and image processing.

Maurizio Falcone (Author), Roberto Ferretti (Author)

9781611973044

Paperback / softback, published 30 November 2013

332 pages
22.9 x 15.2 x 2 cm, 0.593 kg

With numerous applications, particularly in fluid dynamics, the semi-Lagrangian approximation scheme is an essential part of the numerical analyst's toolkit. This largely self-contained book provides a framework for the semi-Lagrangian strategy for 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 cover high-order semi-Lagrangian schemes and their applications to problems in fluid dynamics, front propagation, optimal control, and image processing. The text brings together developments from a wide range of sources to provide a unified treatment of the subject. This book is written for graduate and advanced undergraduate courses on numerical methods, and for researchers and practitioners whose work involves numerical analysis of hyperbolic PDEs.

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

Subject Areas: Miscellaneous items [WZ]