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Exponential perturbative expansions and coordinate transformations
Ana Arnal, Fernando Casas, Cristina Chiralt
We propose a unified approach for different exponential perturbation techniques used in the treatment of time-dependent quantum mechanical problems, namely the Magnus expansion, th…
A unifying framework for perturbative exponential factorizations
Ana Arnal, Fernando Casas, Cristina Chiralt
We propose a framework where Fer and Wilcox expansions for the solution of differential equations are derived from two particular choices for the initial transformation that seeds…
Symmetric-conjugate splitting methods for linear unitary problems
Joackim Bernier, Sergio Blanes, Fernando Casas +1
We analyze the preservation properties of a family of reversible splitting methods when they are applied to the numerical time integration of linear differential equations defined…
A New Optimality Property of Strang's Splitting
Fernando Casas, Jesús María Sanz-Serna, Luke Shaw
For systems of the form , , common in many applications, we analyze splitting integrators based on the (linear/nonlinear) split systems $\dot…
Magnus integrators for linear and quasilinear delay differential equations
Ana Arnal, Fernando Casas, Cristina Chiralt
A procedure to numerically integrate non-autonomous linear delay differential equations is presented. It is based on the use of an spectral discretization of the delayed part to tr…
Runge-Kutta-Nyström symplectic splitting methods of order 8
F. Casas, S. Blanes, A. Escorihuela-Tomàs
Different families of Runge-Kutta-Nyström (RKN) symplectic splitting methods of order 8 are presented for second-order systems of ordinary differential equations and are tested on…