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

Lale Cona; Lale Cona

doi:10.3934/math.2024880

AIMS Mathematics

2024, Volume 9, Issue 7: 18048-18063. doi: 10.3934/math.2024880

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Research article

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

Lale Cona ^,

Gumushane University, Faculty of Engineering and Natural Sciences, Department of Mathematical Engineering, Gumushane, Turkey

Received: 20 March 2024 Revised: 02 May 2024 Accepted: 09 May 2024 Published: 28 May 2024
MSC : 45D05, 47H10

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.
- fixed point,
- nonlinear Volterra integral equations,
- Picard's three step iteration,
- convergence,
- data dependency
Citation: Lale Cona. Convergence and data dependence results of the nonlinear Volterra integral equation by the Picard's three step iteration[J]. AIMS Mathematics, 2024, 9(7): 18048-18063. doi: 10.3934/math.2024880

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Abstract

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.

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