New Numerical Iteration Schemes Based on Perturbation Iteration Algorithms

Simple item page
dc.contributor.authorPakdemirli M.
dc.date.accessioned2024-07-22T08:01:25Z
dc.date.available2024-07-22T08:01:25Z
dc.date.issued2024
dc.description.abstractPerturbation-Iteration algorithms (PIA) have been developed recently to solve differential equations analytically. A continuous solution in terms of closed form functions as an approximation of the original equation can be found using the method. The method has been implemented to algebraic equations, ordinary and partial differential equations successfully. Based on the formalism developed previously, in this work, purely numerical versions of the perturbation-iteration algorithms are proposed for the first time for first-order nonlinear ordinary differential equations. The new algorithms are called as the Numerical Perturbation-Iteration Algorithms (NPIA) to distinguish them from the continuous analytical ones (PIA) and the method in general will be called the Numerical Perturbation-Iteration Method (NPIM). Iteration schemes based on one correction term in the perturbation solution and first-order derivatives in the Taylor series expansions (NPIA(1,1)), and one correction term in the perturbations and second-order derivatives in the series expansions (NPIA(1,2)) are derived. The numerical results are compared with the exact solutions and a very good match is observed. NPIA(1,2) produced slightly better results compared to NPIA(1,1) with total errors being at least O(h2), h being the step size for both methods. An improvement suggestion for NPIA(1,1) is proposed in the last section to eliminate unrealistic blow-up solutions which are encountered for some specific equations. © 2024 World Scientific Publishing Company.
dc.identifier.DOI-ID10.1142/S0219876223500408
dc.identifier.issn02198762
dc.identifier.urihttp://akademikarsiv.cbu.edu.tr:4000/handle/123456789/11445
dc.language.isoEnglish
dc.publisherWorld Scientific
dc.subjectAlgebra
dc.subjectInitial value problems
dc.subjectIterative methods
dc.subjectNonlinear equations
dc.subjectNumerical methods
dc.subjectPerturbation techniques
dc.subjectTaylor series
dc.subjectClosed form
dc.subjectCorrection terms
dc.subjectForm function
dc.subjectInitial-value problem
dc.subjectIteration algorithms
dc.subjectIteration techniques
dc.subjectNumerical iteration
dc.subjectNumerical iteration scheme
dc.subjectNumerical iteration technique
dc.subjectPerturbation–iteration algorithm
dc.subjectOrdinary differential equations
dc.titleNew Numerical Iteration Schemes Based on Perturbation Iteration Algorithms
dc.typeArticle

Files

Collections

Scopus Koleksiyonu