Local Defect Correction Methods for the Bellman Equation
نویسنده
چکیده
We present a multi level method for the Bellman equation of optimal control theory. The so called local defect correction (LDC) method uses a local ne grid to correct the solution in a critical area on the coarse grid. We formulate the method assuming a deterministic state equation and prove convergence and consistency results. Numerical results show, that the LDC method provides an accurate solution with little computational requirement. The LDC method shows also good results, if diierent levels of time discretization are used.
منابع مشابه
An improved collocation method based on deviation of the error for solving BBMB equation
In this paper, we improve b-spline collocation method for Benjamin-Bona-Mahony-Burgers (BBMB) by using defect correction principle. The exact finite difference scheme is used to find defect and the defect correction principle is used to improve collocation method. The method is tested on somemodel problems and the numerical results have been obtained and compared.
متن کاملMultigrid Methods for Second Order Hamilton-Jacobi-Bellman and Hamilton-Jacobi-Bellman-Isaacs Equations
We propose multigrid methods for solving the discrete algebraic equations arising from the discretization of the second order Hamilton–Jacobi–Bellman (HJB) and Hamilton– Jacobi–Bellman–Isaacs (HJBI) equations. We propose a damped-relaxation method as a smoother for multigrid. In contrast with the standard policy iteration, the proposed damped-relaxation scheme is convergent for both HJB and HJB...
متن کاملMultigrid Methods for Hamilton-Jacobi-Bellman and Hamilton-Jacobi-Bellman-Isaacs Equations
We propose multigrid methods for solving Hamilton-Jacobi-Bellman (HJB) and HamiltonJacobi-Bellman-Isaacs (HJBI) equations. The methods are based on the full approximation scheme. We propose a damped-relaxation method as smoother for multigrid. In contrast with policy iteration, the relaxation scheme is convergent for both HJB and HJBI equations. We show by local Fourier analysis that the damped...
متن کاملCan Local Single-Pass Methods Solve Any Stationary Hamilton-Jacobi-Bellman Equation?
The use of local single-pass methods (like, e.g., the Fast Marching method) has become popular in the solution of some Hamilton-Jacobi equations. The prototype of these equations is the eikonal equation, for which the methods can be applied saving CPU time and possibly memory allocation. Then, some natural questions arise: can local single-pass methods solve any HamiltonJacobi equation? If not,...
متن کاملLocal Error Estimates for Moderately Smooth Problems: Part II – SDEs and SDAEs with Small Noise
The paper consists of two parts. In the first part of the paper, we proposed a procedure to estimate local errors of low order methods applied to solve initial value problems in ordinary differential equations (ODEs) and index-1 differential-algebraic equations (DAEs). Based on the idea of Defect Correction we developed local error estimates for the case when the problem data is only moderately...
متن کامل