arXiv subjects

Pep Mulet

Publications and source records attributed to Pep Mulet.

21 records · Page 2Linked to original sources

arXiv2018

On the stability of Approximate Taylor methods for ODE and their relationship with Runge-Kutta schemes

In [Baeza et al., Computers and Fluids, 159, 156--166 (2017)] a new method for the numerical solution of ODEs is presented. This methods can be regarded as an approximate formulation of the Taylor methods and it follows an approach that has a much easier implementation than the original Taylor methods, since only the functions in the ODEs, and not their high order derivatives, are needed. In this reference, the absolute stability region of the new methods is conjectured to be coincident with that of their exact counterparts. There is also a conjecture about their relationship with Runge-Kutta methods. In this work we answer positively both conjectures.

math.NA↗

arXiv2016

Characterization of finite dimensional subspaces of complex functions that are invariant under linear differential operators

The method to solve inhomogeneous linear differential equations that is usually taught at school relies on the fact that the right hand side function is the product of a polynomial and an exponential and that the linear spaces of those functions are invariant under differential operators (finite or ordinary). This short note uses Jordan's canonical decomposition to prove that the linear spaces spanned by products of polynomial and exponentials are the only linear complex spaces that are invariant under differential operators, therefore non-homogeneous linear finite difference or ordinary differential equations can only be generically solved when the right hand side belongs to those spaces.

math.CA↗

arXiv2014

WENO schemes applied to the quasi-relativistic Vlasov--Maxwell model for laser-plasma interaction

In this paper we focus on WENO-based methods for the simulation of the 1D Quasi-Relativistic Vlasov--Maxwell (QRVM) model used to describe how a laser wave interacts with and heats a plasma by penetrating into it. We propose several non-oscillatory methods based on either Runge--Kutta (explicit) or Time-Splitting (implicit) time discretizations. We then show preliminary numerical experiments.

math.AP↗