Nonlinear differential equations with deviating arguments and approximations via a Parker-Sochacki approach

dc.contributor.authorIsaia, Vincenzo M.
dc.date.accessioned2022-04-04T14:42:56Z
dc.date.available2022-04-04T14:42:56Z
dc.date.issued2017-03-08
dc.description.abstractThe Parker-Sochacki method has been successful in generating approximations for a wide variety of ODEs, and even PDEs of evolution type, by achieving an autonomous polynomial vector field and implementing the Picard iteration. The intent of this article is to extend PSM to a large family of differential equations with deviating arguments. Results will be given for problems with delays which are linear in time and state independent, and also have constant initial data and nonlinear differential equations which are retarded, neutral or advanced. The goal of the proofs is to motivate a numerically efficient DDE solver. In addition, an explicit a priori error estimate that does not require derivatives of the vector field is presented. The non-constant initial data cases and the state dependent delay cases are discussed formally.
dc.description.departmentMathematics
dc.formatText
dc.format.extent25 pages
dc.format.medium1 file (.pdf)
dc.identifier.citationIsaia, V. M. (2017). Nonlinear differential equations with deviating arguments and approximations via a Parker-Sochacki approach. <i>Electronic Journal of Differential Equations, 2017</i>(68), pp. 1-25.
dc.identifier.issn1072-6691
dc.identifier.urihttps://hdl.handle.net/10877/15595
dc.language.isoen
dc.publisherTexas State University, Department of Mathematics
dc.rightsAttribution 4.0 International
dc.rights.holderThis work is licensed under a Creative Commons Attribution 4.0 International License.
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.sourceElectronic Journal of Differential Equations, 2017, San Marcos, Texas: Texas State University and University of North Texas.
dc.subjectDelay differential equations
dc.subjectLag
dc.subjectPSM method
dc.subjectMethod of steps
dc.subjectMethod of successive approximation
dc.subjectDeviating argument
dc.titleNonlinear differential equations with deviating arguments and approximations via a Parker-Sochacki approach
dc.typeArticle

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