On a nonlinear integro-differential equation of Fredholm type

Bounaya, Mohammed Charif; Lemita, Samir; Ghiat, Mourad; Aissaoui, Mohamed Zine

doi:10.1504/ijcsm.2021.114188

Cited by 8 publications

(6 citation statements)

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“…However, in Figures (1) and ( 3) we can see that the approximate solutions using option A converge to the exact solutions. Furthermore, Figures (2) and (4) show us the distance between two successive iterates using option A and B for example 1 and 2, respectively, which proves that option A has a linear convergence, worse than option B. So, we conclude that our numerical results are similar to the results of [5], which assure that our vision is reasonable.…”

Section: Numerical Examplessupporting

confidence: 67%

“…where U = (te t , (1 + t)e t ) is its exact solution. However, we solve this system (29) by using option A and compare our results with the results obtained in [2].…”

Section: Numerical Examplesmentioning

confidence: 97%

“…according the technique described in the paper [2], we derive this equation (N − 1) times, then we obtain the system…”

Section: Application On Nonlinear Integro-dierential Equationmentioning

confidence: 99%

“…In this section, to examine the eectiveness of our new process (option A), compared to the classical process (option B), we will treat two examples. In the rst example, we solve by using option A, the same nonlinear Fredholm integro-dierential equation presented in [2], and we compare our results with its results. However, we mention that the results of the paper [2], have been obtained according the classical process (option B).…”

Section: Numerical Examplesmentioning

confidence: 99%

“…In the rst example, we solve by using option A, the same nonlinear Fredholm integro-dierential equation presented in [2], and we compare our results with its results. However, we mention that the results of the paper [2], have been obtained according the classical process (option B). In the second example, we solve a system of nonlinear integral equations by using the both options A and B, also we compare between the obtained results.…”

Section: Numerical Examplesmentioning

confidence: 99%

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Linearization-Discretization process to solve systems of nonlinear Fredholm integral equations in an infinite-dimensional context

Sedka

Lemita

Aissaoui

2022

Advances in the Theory of Nonlinear Analysis and Its Application

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In this paper, we propose a different way for solving systems of nonlinear Fredholm integral equations of the second kind. We construct our new strategy in two steps, through beginning with the linearization phase of the system of Fredholm integral equations by applying Newton method, then we pass to the discretization phase for some involved integral operator using Nystr\"{o}m method. The convergence analysis of our new method is proved under some necessary conditions. At last, a numerical application to approach a nonlinear Fredholm integro-differential equation by using this new process is taken to confirm its advantage.

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Section: Numerical Examplessupporting

confidence: 67%

“…where U = (te t , (1 + t)e t ) is its exact solution. However, we solve this system (29) by using option A and compare our results with the results obtained in [2].…”

Section: Numerical Examplesmentioning

confidence: 97%

“…according the technique described in the paper [2], we derive this equation (N − 1) times, then we obtain the system…”

Section: Application On Nonlinear Integro-dierential Equationmentioning

confidence: 99%

Section: Numerical Examplesmentioning

confidence: 99%

Section: Numerical Examplesmentioning

confidence: 99%

See 3 more Smart Citations