Construccion de metodos exponencialmente ajustados simetricos y
simplecticos de tipo RK Gauss
Luis Rández,
(Universidad de Zaragoza).
Jueves 19 de Noviembre de 2009
The construction of exponentially fitted Runge-Kutta (EFRK) methods
for the numerical integration of Hamiltonian systems with oscillatory
solutions is considered. Based on the symplecticness, symmetry, and
exponential fitting properties, two new three-stage RK integrators of
the Gauss type with fixed or variable nodes, are obtained. The new
exponentially fitted RK Gauss type methods integrate exactly
differential systems whose solutions can be expressed as linear
combinations of the set of functions {exp(?t),exp(-?t)}, The algebraic
order of the new integrators is also analyzed, obtaining that they are
of sixth-order like the classical three-stage RK Gauss method. Some
numerical experiments show that the new methods are more efficient
than the symplectic RK Gauss methods (either standard or else
exponentially fitted) proposed in the scientific literature.