The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods
The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods
High order Runge-Kutta methods on manifolds
proceedings of the on Numerical analysis of hamiltonian differential equations
Practical symplectic partitioned Runge--Kutta and Runge--Kutta--Nyström methods
Journal of Computational and Applied Mathematics
Commutator-free Lie group methods
Future Generation Computer Systems - Special issue: Geometric numerical algorithms
Explicit Exponential Runge-Kutta Methods for Semilinear Parabolic Problems
SIAM Journal on Numerical Analysis
On Magnus Integrators for Time-Dependent Schrödinger Equations
SIAM Journal on Numerical Analysis
A fourth-order commutator-free exponential integrator for nonautonomous differential equations
SIAM Journal on Numerical Analysis
Splitting and composition methods for explicit time dependence in separable dynamical systems
Journal of Computational and Applied Mathematics
High-order commutator-free exponential time-propagation of driven quantum systems
Journal of Computational Physics
Time-averaging and exponential integrators for non-homogeneous linear IVPs and BVPs
Applied Numerical Mathematics
Magnus integrators for solving linear-quadratic differential games
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Hi-index | 0.02 |
We present a family of numerical integrators based on the Magnus series expansions which is designed for solving nonautonomous differential equations. The main difference with standard Magnus integrators is that no commutators are involved. This property allows, in a simple way, to use the methods on non-linear ODEs. Fourth- and sixth-order methods for non-stiff differential equations are studied and new methods are presented. This type of method can easily be tailored to preserve geometric properties of the solutions, and we show through several examples that the performance and error behaviour is significantly better than known methods.