56 citations · 58 across the 5 of their papers we have counts for
7 papers
Multi-rate Runge-Kutta methods: stability analysis and applications
Bernhard Bachmann, Luca Bonaventura, Francesco Casella +3
We present an approach for the efficient implementation of self-adjusting multi-rate Runge-Kutta methods and we introduce a novel stability analysis, that covers the multi-rate ext…
Efficient implicit solvers for models of neuronal networks
Luca Bonaventura, Soledad Fernández-García, Macarena Gómez-Mármol
We introduce economical versions of standard implicit ODE solvers that are specifically tailored for the efficient and accurate simulation of neural networks. These reformulations…
Spectral Variational Multi-Scale method for parabolic problems. Application to 1D transient advection-diffusion equations
Tomás Chacón Rebollo, Soledad Fernández-García, David Moreno-Lopez +1
In this work, we introduce a Variational Multi-Scale (VMS) method for the numerical approximation of parabolic problems, where sub-grid scales are approximated from the eigenpairs…
Saddle-node canard cycles in planar piecewise linear differential systems
Victoriano Carmona, Soledad Fernández-García, Antonio E. Teruel
By applying a singular perturbation approach, canard limit cycles exhibited by a general family of singularly perturbed planar piecewise linear (PWL) differential systems are analy…
VMS spectral solution of two-dimensional advection-diffusion problems with anisotropic velocity
Tomás Chacón Rebollo, Soledad Fernández-García, Macarena Gómez-Mármol
In this article, we extend the Variational Multi-scale method with spectral approximation of the sub-scales to two-dimensional advection-diffusion problems. The spectral VMS method…
Variational multi-scale spectral solution of convection-dominated parabolic problems
Tomás Chacón Rebollo, Soledad Fernández-García
In this work, we consider an extension to parabolic problems of the variational multiscale method with spectral approximation of the sub-scales. We first discretize in time using a…