Reliable Iterative Method for solving Volterra -Fredholm Integro Differential Equations

Marez, Samaher

doi:10.29350/qjps.2021.26.2.1262

Cited by 3 publications

(2 citation statements)

References 10 publications

(5 reference statements)

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“…The iterative method (IM) was presented by Temimi and Ansari [17], it was successfully used for solving nonlinear and linear functional equations, ordinary differential equations (ODEs), partial differential equations (PDEs), higher-order integro differential equations (HOIDEs), nonlinear delay differential equations(NDDEs), Korteweg-de Vries equations (KdVs) and Volterra -Fredholm integro differential equations (VFIDEs), see [18][19][20][21][22][23].…”

Section: Yasseinmentioning

confidence: 99%

Modified Iterative Method for Solving Sine - Gordon Equations

Yassein

2023

Iraqi Journal of Science

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The basic goal of this research is to utilize an analytical method which is called the Modified Iterative Method in order to gain an approximate analytic solution to the Sine-Gordon equation. The suggested method is the amalgamation of the iterative method and a well-known technique, namely the Adomian decomposition method. A method minimizes the computational size, averts round-off errors, transformation and linearization, or takes some restrictive assumptions. Several examples are chosen to show the importance and effectiveness of the proposed method. In addition, a modified iterative method gives faster and easier solutions than other methods. These solutions are accurate and in agreement with the series of solutions that are provided by analytical results. To evaluate the outcomes in the modified iterative process, we have used the Matlab symbolic manipulator.

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Section: Yasseinmentioning

confidence: 99%

Modified Iterative Method for Solving Sine - Gordon Equations

Yassein

2023

Iraqi Journal of Science

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“…Lotfi and Alipanah (2020) describes the Legendre spectral element method for solving integrodifferential equations. Samaher (2021) proposes a reliable iterative method for resolving many types of Volterra-Fredholm integrodifferential equations, and the iterative method is used to obtain series solutions to the problems under consideration. Adebisi et al (2021) employed the Galerkin method to solve Volterra integrodifferntial equations using Chebyshev polynomials as the basis function.…”

Section: Introductionmentioning

confidence: 99%

A New Numerical Approach Using Chebyshev Third Kind Polynomial for Solving Integrodifferential Equations of Higher Order

Abdullahi

James

ISHAQ>

et al. 2022

Gazi University Journal of Science Part A: Engineering and Innovation

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There are several classifications of linear Integral Equations. Some of them include; Voltera Integral Equations, Fredholm Linear Integral Equations, Fredholm-Voltera Integrodifferential. In the past, solutions of higher-order Fredholm-Volterra Integrodifferential Equations [FVIE] have been presented. However, this work uses a computational techniques premised on the third kind Chebyshev polynomials method. The performance of the results for distinctive degrees of approximation (M) of the trial solution is cautiously studied and comparisons have been additionally made between the approximate/estimated and exact/definite solution at different intervals of the problems under consideration. Modelled Problems have been provided to illustrate the performance and relevance of the techniques. However, it turned out that as M increases, the outcomes received after every iteration get closer to the exact solution in all of the problems considered. The results of the experiments are therefore visible from the tables of errors and the graphical representation presented in this work.

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Numerical Solutions of Nonlinear Fredholm Integro Differential Equations using Fifth Order Runge-kutta Method

Saleh

Barghooth

Rasheed

2021

J. Phys.: Conf. Ser.

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This paper is considered with the numerical solution of a type of second-order nonlinear Fredholm integro-differential Equations (FIDs). The proposed scheme is based on Runge - kutta methods of order fifth. Moreover, two numerical examples are considered to show the capability and the accuracy of the proposed methods compared with other Runge-kutta methods of less order. Finally, we apply the least square errors (LSE) formula to make numerical comparisons between the numerical and the exact solutions. The obtained results show that the proposed method is superior and more accurate than Runge - kutta methods of orders two, three, and four.

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Reliable Iterative Method for solving Volterra -Fredholm Integro Differential Equations

Cited by 3 publications

References 10 publications

Modified Iterative Method for Solving Sine - Gordon Equations

Modified Iterative Method for Solving Sine - Gordon Equations

A New Numerical Approach Using Chebyshev Third Kind Polynomial for Solving Integrodifferential Equations of Higher Order

Numerical Solutions of Nonlinear Fredholm Integro Differential Equations using Fifth Order Runge-kutta Method

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