Bader, Philipp Karl Heinz; Blanes Zamora, Sergio; Casas, Fernando; Ponsoda Miralles, Enrique(Elsevier, 2016-01-01)
We consider the numerical integration of high-order linear non-homogeneous differential
equations, written as first order homogeneous linear equations, and using exponential
methods. Integrators like Magnus expansions ...
We consider the numerical integration of coupled self-adjoint non-autonomous partial differential systems. Under convergence conditions, the solution can be written as a series expansion where each of its terms correspond ...
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 ...
The analysis of heat conduction through a solid with heat generation leads to a linear matrix differential equation with separated boundary conditions. We present a symmetric second order exponential integrator for the ...
Ponsoda Miralles, Enrique(Universitat Politècnica de València, 2009-06-03)
EN ESTA MEMORIA SE CONSIDERAN DOS TIPOS DE ECUACIONES DIFERENCIALES MATRICIALES. EN PRIMER LUGAR SE CONSTRUYEN SOLUCIONES NUMERICAS PARA PROBLEMAS DE VALORES INICIALES MATRICIALES UTILIZANDO METODOS LINEALES MULTIPASO ...
[EN] We present structure preserving integrators for solving linear quadratic optimal control
problems. The goal is to build methods which can also be used for the integration of
nonlinear problems if they are previously ...
[EN] Two families of symplectic methods specially designed for second-order time-dependent linear systems are presented. Both are obtained from the Magnus expansion of the corresponding first-order equation, but otherwise ...
[EN] We consider the numerical integration of the matrix Hill equation. Parametric resonances
can appear and this property is of great interest in many different physical applications.
Usually, Hill s equations originate ...
We consider time-averaging methods based on the Magnus series expansion jointly with exponential integrators for the numerical integration of general linear non-homogeneous differential equations. The schemes can be ...