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

2014-01-31 Mathematics
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Release : 2014-01-31
Genre : Mathematics
Kind : eBook
Book Rating : 04X/5 ( reviews)

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Book Synopsis Semi-Lagrangian Approximation Schemes for Linear and Hamilton-Jacobi Equations by : Maurizio Falcone

Download or read book Semi-Lagrangian Approximation Schemes for Linear and Hamilton-Jacobi Equations written by Maurizio Falcone. This book was released on 2014-01-31. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Hamilton-Jacobi-Bellman Equations

2018-08-06 Mathematics
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Release : 2018-08-06
Genre : Mathematics
Kind : eBook
Book Rating : 591/5 ( reviews)

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Book Synopsis Hamilton-Jacobi-Bellman Equations by : Dante Kalise

Download or read book Hamilton-Jacobi-Bellman Equations written by Dante Kalise. This book was released on 2018-08-06. Available in PDF, EPUB and Kindle. Book excerpt: Optimal feedback control arises in different areas such as aerospace engineering, chemical processing, resource economics, etc. In this context, the application of dynamic programming techniques leads to the solution of fully nonlinear Hamilton-Jacobi-Bellman equations. This book presents the state of the art in the numerical approximation of Hamilton-Jacobi-Bellman equations, including post-processing of Galerkin methods, high-order methods, boundary treatment in semi-Lagrangian schemes, reduced basis methods, comparison principles for viscosity solutions, max-plus methods, and the numerical approximation of Monge-Ampère equations. This book also features applications in the simulation of adaptive controllers and the control of nonlinear delay differential equations. Contents From a monotone probabilistic scheme to a probabilistic max-plus algorithm for solving Hamilton–Jacobi–Bellman equations Improving policies for Hamilton–Jacobi–Bellman equations by postprocessing Viability approach to simulation of an adaptive controller Galerkin approximations for the optimal control of nonlinear delay differential equations Efficient higher order time discretization schemes for Hamilton–Jacobi–Bellman equations based on diagonally implicit symplectic Runge–Kutta methods Numerical solution of the simple Monge–Ampere equation with nonconvex Dirichlet data on nonconvex domains On the notion of boundary conditions in comparison principles for viscosity solutions Boundary mesh refinement for semi-Lagrangian schemes A reduced basis method for the Hamilton–Jacobi–Bellman equation within the European Union Emission Trading Scheme

Approximation Schemes for Viscosity Solutions of Hamilton-Jacobi Equations

1983 Hamilton-Jacobi equations
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Release : 1983
Genre : Hamilton-Jacobi equations
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Book Synopsis Approximation Schemes for Viscosity Solutions of Hamilton-Jacobi Equations by : Panagiotis E. Souganidis

Download or read book Approximation Schemes for Viscosity Solutions of Hamilton-Jacobi Equations written by Panagiotis E. Souganidis. This book was released on 1983. Available in PDF, EPUB and Kindle. Book excerpt: Equations of Hamilton-Jacobi type arise in many areas of application, including the calculus of variations of variations, control theory and differential games. Recently Crandall and Lions established the correct notion of generalized solutions for these equations. This article discusses the convergence of general approximation schemes to this solution and gives, under certain hypotheses, explicit error estimates. These results are then applied to obtain various representations. These include max-min representations of solutions relevant to the theory of differential games (which imply the existence of the value of the game), representations as limits of solutions of general explicit and implicit finite difference schemes, and as limits of several types of Trotter products. (Author).

Hamilton-Jacobi Equations: Approximations, Numerical Analysis and Applications

2013-05-24 Mathematics
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Release : 2013-05-24
Genre : Mathematics
Kind : eBook
Book Rating : 330/5 ( reviews)

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Book Synopsis Hamilton-Jacobi Equations: Approximations, Numerical Analysis and Applications by : Yves Achdou

Download or read book Hamilton-Jacobi Equations: Approximations, Numerical Analysis and Applications written by Yves Achdou. This book was released on 2013-05-24. Available in PDF, EPUB and Kindle. Book excerpt: These Lecture Notes contain the material relative to the courses given at the CIME summer school held in Cetraro, Italy from August 29 to September 3, 2011. The topic was "Hamilton-Jacobi Equations: Approximations, Numerical Analysis and Applications". The courses dealt mostly with the following subjects: first order and second order Hamilton-Jacobi-Bellman equations, properties of viscosity solutions, asymptotic behaviors, mean field games, approximation and numerical methods, idempotent analysis. The content of the courses ranged from an introduction to viscosity solutions to quite advanced topics, at the cutting edge of research in the field. We believe that they opened perspectives on new and delicate issues. These lecture notes contain four contributions by Yves Achdou (Finite Difference Methods for Mean Field Games), Guy Barles (An Introduction to the Theory of Viscosity Solutions for First-order Hamilton-Jacobi Equations and Applications), Hitoshi Ishii (A Short Introduction to Viscosity Solutions and the Large Time Behavior of Solutions of Hamilton-Jacobi Equations) and Grigory Litvinov (Idempotent/Tropical Analysis, the Hamilton-Jacobi and Bellman Equations).

Numerical Methods For Viscosity Solutions And Applications

2001-08-30 Mathematics
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Release : 2001-08-30
Genre : Mathematics
Kind : eBook
Book Rating : 377/5 ( reviews)

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Book Synopsis Numerical Methods For Viscosity Solutions And Applications by : Maurizio Falcone

Download or read book Numerical Methods For Viscosity Solutions And Applications written by Maurizio Falcone. This book was released on 2001-08-30. Available in PDF, EPUB and Kindle. Book excerpt: The volume contains twelve papers dealing with the approximation of first and second order problems which arise in many fields of application including optimal control, image processing, geometrical optics and front propagation. Some contributions deal with new algorithms and technical issues related to their implementation. Other contributions are more theoretical, dealing with the convergence of approximation schemes. Many test problems have been examined to evaluate the performances of the algorithms. The volume can attract readers involved in the numerical approximation of differential models in the above-mentioned fields of applications, engineers, graduate students as well as researchers in numerical analysis.

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