Volterra Systems with Realizable Kernels

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dc.contributor.authorNguyen, Hoan Kim Huynhen
dc.contributor.committeechairHerdman, Terry L.en
dc.contributor.committeememberRogers, Robert C.en
dc.contributor.committeememberBorggaard, Jeffrey T.en
dc.contributor.committeememberCliff, Eugene M.en
dc.contributor.committeememberBurns, John A.en
dc.contributor.departmentMathematicsen
dc.date.accessioned2011-08-22T19:00:56Zen
dc.date.adate2004-04-30en
dc.date.available2011-08-22T19:00:56Zen
dc.date.issued2004-04-12en
dc.date.rdate2007-04-30en
dc.date.sdate2004-04-29en
dc.description.abstractWe compare an internal state method and a direct Runge-Kutta method for solving Volterra integro-differential equations and Volterra delay differential equations. The internal state method requires the kernel of the Volterra integral to be realizable as an impulse response function. We discover that when applicable, the internal state method is orders of magnitude more efficient than the direct numerical method. However, constructing state representation for realizable kernels can be challenging at times; therefore, we propose a rational approximation approach to avoid the problem. That is, we approximate the transfer function by a rational function, construct the corresponding linear system, and then approximate the Volterra integro-differential equation. We show that our method is convergent for the case where the kernel is nuclear. We focus our attention on time-invariant realizations but the case where the state representation of the kernel is a time-variant linear system is briefly discussed.en
dc.description.degreePh. D.en
dc.format.mediumETDen
dc.identifier.otheretd-04292004-143629en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-04292004-143629en
dc.identifier.urihttp://hdl.handle.net/10919/11153en
dc.publisherVirginia Techen
dc.relation.haspartetd.pdfen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectVolterra Integro-Differential Equationsen
dc.subjectRunge-Kutta Methoden
dc.subjectRealization Theoryen
dc.subjectDelay Equationsen
dc.subjectInternal Stateen
dc.titleVolterra Systems with Realizable Kernelsen
dc.typeDissertationen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.namePh. D.en

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