Animaciones en Matlab y maple de ecuaciones diferenciales parciales de la física-matemática

Abstract

In this work we present some exact solutions of time dependent partial differential equations (pdes); these solutions have the general form $u(x,t)$, with $x\in \mathcal{ R}^n$, $n=1,2,3$. The plots of the solutions at different times allow us to create animations of the solutions. We show in a general framework how to make animations in Maple and Matlab. These animations can be used as a didactic tool in order to introduce some physical phenomena such as: wave propagation, superposition, transmission from one medium to another, diffusion, etc. They can also be used to motive the students to the study of partial differential equations and its applications. A representative subset of differential equations of mathematical physics was chosen that includes: the transport equation, wave equation, heat equation and equations of Klein Gordon, Korteweg de Vries, and Maxwell. We briefly present some of the analytical methods for the solutions of pdes: scaling, characteristics and separation of variables. Finally exact solutions can be very useful for code testing in numerical implementations.