Legendre spectral element method for solving Volterra-integro differential equations

Lotfi, Mahmoud; Alipanah, Amjad

doi:10.1016/j.rinam.2020.100116

Cited by 10 publications

(6 citation statements)

References 17 publications

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“…Definition 1. We call an ε-approximate polynomial solution of the problem (1) + (2) an approximate polynomial solution x app , satisfying the relations (6) and (7).…”

Section: The Methodsmentioning

confidence: 99%

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The Polynomial Least Squares Method for Nonlinear Fractional Volterra and Fredholm Integro-Differential Equations

Căruntu

Paşca

2021

Mathematics

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“…Definition 1. We call an ε-approximate polynomial solution of the problem (1) + (2) an approximate polynomial solution x app , satisfying the relations (6) and (7).…”

Section: The Methodsmentioning

confidence: 99%

“…The Legendre Spectral Element Method, employed by Lotfi and Alipanah in 2020 (( [7]) to solve Volterra-Fredholm integro-differential equations, •…”

Section: Introductionmentioning

confidence: 99%

The Polynomial Least Squares Method for Nonlinear Fractional Volterra and Fredholm Integro-Differential Equations

Căruntu

Paşca

2021

Mathematics

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“…Rabiei et al (2019) investigated the numerical solution of Volterra integrodifferential equations using the General linear method; in the work, the order conditions of the proposed method are derived using B-series and rooted trees techniques. 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.…”

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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“…Zhou and Xu [14] introduced numerical solution of FVFIDEs with mixed boundary conditions using the Chebyshev wavelet method; Dehestani et al [15] used a combination of Lucas wavelets and Legendre-Gauss quadrature; Salman and Mustafa [16] used Lagrange polynomials; Rajagopal et al [17] applied a new numerical method for FIDEs; Lotfi and Alipanah [18] employed the Legendre spectral element method for solving Volterraintegro differential equations. Also, Meng et…”

Section: Introductionmentioning

confidence: 99%

Second kind Chebyshev collocation technique for Volterra-Fredholm fractional order integro-differential equations

Oyedepo

Ayoade

Otaide

et al. 2022

J. Nat. Scien. & Math. Res.

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In this work, we present the numerical solution of fractional order Volterra–Fredholm integro-differential equations using the second kind of Chebyshev collocation technique. First, we transformed the problem into a system of linear algebraic equations, which are then solved using matrix inversion to obtain the unknown constants. Furthermore, numerical examples are used to outline the method’s accuracy and efficiency using tables and figures. The results show that the method performed better in terms of improving accuracy and requiring less rigorous work.©2022 JNSMR UIN Walisongo. All rights reserved.

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Legendre spectral element method for solving Volterra-integro differential equations

Cited by 10 publications

References 17 publications

The Polynomial Least Squares Method for Nonlinear Fractional Volterra and Fredholm Integro-Differential Equations

The Polynomial Least Squares Method for Nonlinear Fractional Volterra and Fredholm Integro-Differential Equations

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

Second kind Chebyshev collocation technique for Volterra-Fredholm fractional order integro-differential equations

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