A resolution method for Riccati differential systems coupled in their quadratic terms
SIAM Journal on Mathematical Analysis
Optimal control: linear quadratic methods
Optimal control: linear quadratic methods
Numerical integration of the differential Riccati equation and some related issues
SIAM Journal on Numerical Analysis
The Riccati equation
Expokit: a software package for computing matrix exponentials
ACM Transactions on Mathematical Software (TOMS)
A Natural Approach to the Numerical Integration of Riccati Differential Equations
SIAM Journal on Numerical Analysis
Approximating the exponential from a Lie algebra to a Lie group
Mathematics of Computation
Differential games in economics and management science
Differential games in economics and management science
Applied Numerical Mathematics
High-order commutator-free exponential time-propagation of driven quantum systems
Journal of Computational Physics
Approximate solutions with a priori error bounds for continuous coefficient matrix Riccati equations
Mathematical and Computer Modelling: An International Journal
Time-averaging and exponential integrators for non-homogeneous linear IVPs and BVPs
Applied Numerical Mathematics
Journal of Computational and Applied Mathematics
| Hi-index | 7.29 |
We consider Magnus integrators to solve linear-quadratic N-player differential games. These problems require to solve, backward in time, non-autonomous matrix Riccati differential equations which are coupled with the linear differential equations for the dynamic state of the game, to be integrated forward in time. We analyze different Magnus integrators which can provide either analytical or numerical approximations to the equations. They can be considered as time-averaging methods and frequently are used as exponential integrators. We show that they preserve some of the most relevant qualitative properties of the solution for the matrix Riccati differential equations as well as for the remaining equations. The analytical approximations allow us to study the problem in terms of the parameters involved. Some numerical examples are also considered which show that exponential methods are, in general, superior to standard methods.