Numerical solution of nonlinear complex integral equations using quasi- wavelets

Ahmed Ayad Khudhair; Saeed Sohrabi; Hamid Ranjbar; Ahmed Ayad Khudhair; Saeed Sohrabi; Hamid Ranjbar

doi:10.3934/math.20241638

AIMS Mathematics

2024, Volume 9, Issue 12: 34387-34405. doi: 10.3934/math.20241638

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Research article

Numerical solution of nonlinear complex integral equations using quasi- wavelets

Department of Mathematics, Faculty of Science, Urmia University, Urmia 57561-51818, Iran

Received: 14 August 2024 Revised: 11 November 2024 Accepted: 26 November 2024 Published: 06 December 2024
MSC : 65N35, 65R20, 65T60

In this paper, we introduced a numerical approach for estimating the solutions of nonlinear Fredholm integral equations in the complex plane. The main problem was transformed into a novel integral equation, which simplified the computation of integrals derived from the discretization technique. The combination of the standard collocation method with periodic quasi-wavelets, as well as their fundamental properties, was utilized to convert the solution of the newly formulated integral equation into a nonlinear complex system of algebraic equations. The convergence properties of the scheme were also presented. Finally, several numerical examples were provided to demonstrate the efficiency and precision of our proposed approach, which also confirmed its superiority over polynomial collocation methods.
- collocation method,
- Hammerstein integral equation,
- periodic quasi-wavelets,
- complex plane,
- convergence
Citation: Ahmed Ayad Khudhair, Saeed Sohrabi, Hamid Ranjbar. Numerical solution of nonlinear complex integral equations using quasi- wavelets[J]. AIMS Mathematics, 2024, 9(12): 34387-34405. doi: 10.3934/math.20241638

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Abstract

In this paper, we introduced a numerical approach for estimating the solutions of nonlinear Fredholm integral equations in the complex plane. The main problem was transformed into a novel integral equation, which simplified the computation of integrals derived from the discretization technique. The combination of the standard collocation method with periodic quasi-wavelets, as well as their fundamental properties, was utilized to convert the solution of the newly formulated integral equation into a nonlinear complex system of algebraic equations. The convergence properties of the scheme were also presented. Finally, several numerical examples were provided to demonstrate the efficiency and precision of our proposed approach, which also confirmed its superiority over polynomial collocation methods.

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