Solution of second order differential equations using the Godunov integration method

Persistent Link:
http://hdl.handle.net/10150/277319
Title:
Solution of second order differential equations using the Godunov integration method
Author:
Beamis, Christopher Paul, 1960-
Issue Date:
1990
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
This MS Thesis proposes the use of an integration technique due to Godunov for the direct numerical solution of systems of second order differential equations. This method is to be used instead of the conventional technique of separating each second order equation into two first order equations and then solving the resulting system with one of the many methods available for systems of first order differential equations. Stability domains and expressions for the truncation error will be developed for this method when it is used to solve the wave equation, a passive mechanical system, and a passive electrical circuit. It will be shown both analytically and experimentally that the Godunov method compares favorably with the Adams-Bashforth third order method when used to solve both the wave equation and the mechanical system, but that there are potential problems when this method is used to simulate electrical circuits which result in integro-differential equations.
Type:
text; Thesis-Reproduction (electronic)
Keywords:
Mathematics.; Engineering, Electronics and Electrical.; Engineering, Mechanical.
Degree Name:
M.S.
Degree Level:
masters
Degree Program:
Graduate College
Degree Grantor:
University of Arizona
Advisor:
Cellier, Francois E.

Full metadata record

DC FieldValue Language
dc.language.isoen_USen_US
dc.titleSolution of second order differential equations using the Godunov integration methoden_US
dc.creatorBeamis, Christopher Paul, 1960-en_US
dc.contributor.authorBeamis, Christopher Paul, 1960-en_US
dc.date.issued1990en_US
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.abstractThis MS Thesis proposes the use of an integration technique due to Godunov for the direct numerical solution of systems of second order differential equations. This method is to be used instead of the conventional technique of separating each second order equation into two first order equations and then solving the resulting system with one of the many methods available for systems of first order differential equations. Stability domains and expressions for the truncation error will be developed for this method when it is used to solve the wave equation, a passive mechanical system, and a passive electrical circuit. It will be shown both analytically and experimentally that the Godunov method compares favorably with the Adams-Bashforth third order method when used to solve both the wave equation and the mechanical system, but that there are potential problems when this method is used to simulate electrical circuits which result in integro-differential equations.en_US
dc.typetexten_US
dc.typeThesis-Reproduction (electronic)en_US
dc.subjectMathematics.en_US
dc.subjectEngineering, Electronics and Electrical.en_US
dc.subjectEngineering, Mechanical.en_US
thesis.degree.nameM.S.en_US
thesis.degree.levelmastersen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorCellier, Francois E.en_US
dc.identifier.proquest1341224en_US
dc.identifier.bibrecord.b26330763en_US
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