Opis: Semi-Lagrangian Approximation Schemes for Linear and Hamilton-Jacobi Equations - Roberto Ferretti, Maurizio Falcone

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.

Szczegóły: Semi-Lagrangian Approximation Schemes for Linear and Hamilton-Jacobi Equations - Roberto Ferretti, Maurizio Falcone

Tytuł: Semi-Lagrangian Approximation Schemes for Linear and Hamilton-Jacobi Equations
Autor: Roberto Ferretti, Maurizio Falcone
Producent: Society of Industrial and Applied Mathematics U.S
ISBN: 9781611973044
Rok produkcji: 2014
Ilość stron: 330
Oprawa: Miękka
Waga: 0.58 kg

Recenzje: Semi-Lagrangian Approximation Schemes for Linear and Hamilton-Jacobi Equations - Roberto Ferretti, Maurizio Falcone