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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.identifier.citationIsaia, V. M. (2017). Nonlinear differential equations with deviating arguments and approximations via a Parker-Sochacki approach. Electronic Journal of Differential Equations, 2017(68), pp. 1-25.en_US
dc.identifier.issn1072-6691
dc.identifier.urihttps://digital.library.txstate.edu/handle/10877/15595
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.en_US
dc.formatText
dc.format.extent25 pages
dc.format.medium1 file (.pdf)
dc.language.isoenen_US
dc.publisherTexas State University, Department of Mathematicsen_US
dc.sourceElectronic Journal of Differential Equations, 2017, San Marcos, Texas: Texas State University and University of North Texas.
dc.subjectDelay differential equationsen_US
dc.subjectLagen_US
dc.subjectPSM methoden_US
dc.subjectMethod of stepsen_US
dc.subjectMethod of successive approximationen_US
dc.subjectDeviating argumenten_US
dc.titleNonlinear differential equations with deviating arguments and approximations via a Parker-Sochacki approachen_US
dc.typepublishedVersion
txstate.documenttypeArticle
dc.rights.licenseCreative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.


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