El grupo de Física de los Sistemas Complejos les invita al siguiente seminario presencial y online. Ponente: Prof. Pedro Garrido. Universidad de Granada. Título: A ghost perturbation scheme to solve ordinary differential equations. Resumen: We propose an algebraic method to systematically approach the solution of an ordinary dif- ferential equation (ODE) with any boundary conditions. We define an extended ODE (eODE) composed of a linear generic differential operator that depends on free parameters plus an ε formal perturbation formed by the original ODE minus the same linear term. After an eODE’s formal ε expansion, we can solve order by order a hierarchy of linear ODEs. We get a sequence of functions that converge exponentially fast to the solution/s when ε = 1 and after determining the free set of parameters by minimising a distance-to-the solution function. Therefore, we get a formal expan- sion of the solution that we call Ghost Expansion that can be used as a multiscaling decomposition of the ODE’s solution. The method permits the detection of several solutions to Boundary Value Problems just by looking at the number of minima of the distance function. We present the method by its application to several cases where we discuss its properties, benefits and shortcomings and some practical algorithmic improvements on it. Lugar: Aula de Física Computacional. Facultad de Ciencias. Fecha y hora: Miércoles 1 de junio. 11:00. Enlace: https://meet.google.com/xid-qwsk-iqf https://meet.google.com/xid-qwsk-iqf --------------------------------------------------------------------------------- Daniel Manzano Electromagnetism and Condensed Matter Department Institute “Carlos I” for Theoretical and Computational Physics University of Granada Facultad de Ciencias, Av. Fuentenueva s/n Granada 18071, Spain Phone: +34 958241000 Ext: 20569 http://ic1.ugr.es/manzano/ http://ic1.ugr.es/manzano/