Resolution of First- and Second-Order Linear Differential Equations with Periodic Inputs by a Computer Algebra System

Resolution of First- and Second-Order Linear Differential Equations with Periodic Inputs by a Computer Algebra System

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...

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Main Authors: M. Legua, I. Morales, L. M. Sánchez Ruiz
Format: Article
Language:English
Published: Hindawi Limited 2008-01-01
Series:Mathematical Problems in Engineering
Online Access:http://dx.doi.org/10.1155/2008/654820
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spelling doaj-8604983a3ff240b39e5aaf025668b9d32020-11-24T23:18:45ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472008-01-01200810.1155/2008/654820654820Resolution of First- and Second-Order Linear Differential Equations with Periodic Inputs by a Computer Algebra SystemM. Legua0I. Morales1L. M. Sánchez Ruiz2Departamento de Matemática Aplicada, Centro Politécnico Superior (CPS), Universidad de Zaragoza, 50015 Zaragoza, SpainDepartamento de Matemática Aplicada, Escuela Técnica Superior de Ingenieros Agrónomos (ETSIA), and (IUMPA), Universidad Politécnica de Valencia, 46022 Valencia, SpainDepartamento 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, SpainIn 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.http://dx.doi.org/10.1155/2008/654820
collection DOAJ
language English
format Article
sources DOAJ
author M. Legua
I. Morales
L. M. Sánchez Ruiz
spellingShingle M. Legua
I. Morales
L. M. Sánchez Ruiz
Resolution of First- and Second-Order Linear Differential Equations with Periodic Inputs by a Computer Algebra System
Mathematical Problems in Engineering
author_facet M. Legua
I. Morales
L. M. Sánchez Ruiz
author_sort M. Legua
title Resolution of First- and Second-Order Linear Differential Equations with Periodic Inputs by a Computer Algebra System
title_short Resolution of First- and Second-Order Linear Differential Equations with Periodic Inputs by a Computer Algebra System
title_full Resolution of First- and Second-Order Linear Differential Equations with Periodic Inputs by a Computer Algebra System
title_fullStr Resolution of First- and Second-Order Linear Differential Equations with Periodic Inputs by a Computer Algebra System
title_full_unstemmed Resolution of First- and Second-Order Linear Differential Equations with Periodic Inputs by a Computer Algebra System
title_sort resolution of first- and second-order linear differential equations with periodic inputs by a computer algebra system
publisher Hindawi Limited
series Mathematical Problems in Engineering
issn 1024-123X
1563-5147
publishDate 2008-01-01
description 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.
url http://dx.doi.org/10.1155/2008/654820
work_keys_str_mv AT mlegua resolutionoffirstandsecondorderlineardifferentialequationswithperiodicinputsbyacomputeralgebrasystem
AT imorales resolutionoffirstandsecondorderlineardifferentialequationswithperiodicinputsbyacomputeralgebrasystem
AT lmsanchezruiz resolutionoffirstandsecondorderlineardifferentialequationswithperiodicinputsbyacomputeralgebrasystem
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