Semi-Lagrangian Approximation Schemes for Linear and Hamilton-Jacobi Equations
Author: Maurizio Falcone
Publisher: SIAM
Published: 2014-01-31
Total Pages: 331
ISBN-13: 161197304X
DOWNLOAD EBOOK →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.