Mathematical Problems in Engineering
Volume 2008 (2008), Article ID 654820, 7 pages
doi:10.1155/2008/654820
Research Article
Resolution of First- and Second-Order Linear Differential Equations with Periodic Inputs by a Computer Algebra System
1Departamento de Matemática Aplicada, Centro Politécnico Superior (CPS), Universidad de Zaragoza, 50015 Zaragoza, Spain
2Departamento de Matemática Aplicada, Escuela Técnica Superior de Ingenieros Agrónomos (ETSIA), and (IUMPA), Universidad Politécnica de Valencia, 46022 Valencia, Spain
3Departamento de Matemática Aplicada, Escuela Técnica Superior de Ingeniería del Diseño (ETSID), and Instituto Universitario de Matemática Pura y Aplicada (IUMPA), Universidad Politécnica de Valencia, 46022 Valencia, Spain
Received 16 June 2008; Accepted 26 July 2008
Academic Editor: Carlo Cattani
Copyright © 2008 M. Legua et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
In signal processing, a pulse means a rapid change in the amplitude
of a signal from a baseline value to a higher or lower value, followed by a
rapid return to the baseline value. A square wave function may be viewed
as a pulse that repeats its occurrence periodically but the return to the
baseline value takes some time to happen. When these periodic functions
act as inputs in dynamic systems, the standard tool commonly used to
solve the associated initial value problem (IVP) is Laplace transform and
its inverse. We show how a computer algebra system may
also provide the solution of these IVP straight forwardly by adequately
introducing the periodic input.