scholarly journals 5. Efficient Higher Order Time Discretization Schemes For Hamilton–Jacobi–Bellman Equations Based On Diagonally Implicit Symplectic Runge–Kutta Methods

2018 ◽  
pp. 97-128
Keyword(s):  
Time Discretization ◽  
Higher Order ◽  
Bellman Equations ◽  
Discretization Schemes ◽  
Runge Kutta ◽  
Hamilton Jacobi Bellman

scholarly journals On the Accuracy and Efficiency of Transient Spectral Element Models for Seismic Wave Problems

2016 ◽  
Vol 2016 ◽  
pp. 1-15 ◽  
Author(s):  
Sanna Mönkölä
Keyword(s):  
Fourth Order ◽  
Wave Equations ◽  
Seismic Waves ◽  
Time Discretization ◽  
Spectral Element ◽  
Higher Order ◽  
Time Stepping ◽  
Discretization Schemes ◽  
Elastic Wave Equations ◽  
Wave Problems

This study concentrates on transient multiphysical wave problems for simulating seismic waves. The presented models cover the coupling between elastic wave equations in solid structures and acoustic wave equations in fluids. We focus especially on the accuracy and efficiency of the numerical solution based on higher-order discretizations. The spatial discretization is performed by the spectral element method. For time discretization we compare three different schemes. The efficiency of the higher-order time discretization schemes depends on several factors which we discuss by presenting numerical experiments with the fourth-order Runge-Kutta and the fourth-order Adams-Bashforth time-stepping. We generate a synthetic seismogram and demonstrate its function by a numerical simulation.

scholarly journals Policy iteration for Hamilton–Jacobi–Bellman equations with control constraints

2021 ◽  
Author(s):  
Sudeep Kundu ◽  
Karl Kunisch
Keyword(s):  
Linear Equations ◽  
Hjb Equation ◽  
Policy Iteration ◽  
Optimal Feedback Control ◽  
Iteration Step ◽  
Control Constraints ◽  
Hjb Equations ◽  
Bellman Equations ◽  
Hamilton Jacobi Bellman ◽  
Feedback Control Theory

AbstractPolicy iteration is a widely used technique to solve the Hamilton Jacobi Bellman (HJB) equation, which arises from nonlinear optimal feedback control theory. Its convergence analysis has attracted much attention in the unconstrained case. Here we analyze the case with control constraints both for the HJB equations which arise in deterministic and in stochastic control cases. The linear equations in each iteration step are solved by an implicit upwind scheme. Numerical examples are conducted to solve the HJB equation with control constraints and comparisons are shown with the unconstrained cases.

Sign in / Sign up

Export Citation Format

Share Document