Convergence and data dependence results of the nonlinear Volterra integral equation by the Picard's three step iteration

Picard's three step iteration algorithm was one of the iteration algorithms that was recently shown to be faster than some other iterative algorithms in the existing literature. The purpose of this paper was to study using this iteration algorithm for the solution of nonlinear Volterra integral...

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Bibliographic Details
Published inAIMS mathematics Vol. 9; no. 7; pp. 18048 - 18063
Main Author Cona, Lale
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2024
Subjects
convergence
data dependency
fixed point
nonlinear volterra integral equations
picard's three step iteration
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Summary:Picard's three step iteration algorithm was one of the iteration algorithms that was recently shown to be faster than some other iterative algorithms in the existing literature. The purpose of this paper was to study using this iteration algorithm for the solution of nonlinear Volterra integral equations. It was investigated that the sequences obtained from this iteration algorithm converged to the solution of nonlinear Volterra integral equations. Moreover, data dependence was obtained for nonlinear Volterra integral equations. An example was given that confirmed the applicability of the newly proven theorems.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2024880