Spectral technique with convergence analysis for solving one and two-dimensional mixed Volterra-Fredholm integral equation

Amin, A. Z. M.; Amin, Atul K.; Abdelkawy, Mohamed; Alluhaybi, Ahmad A.; Hashim, Ishak

doi:10.1371/journal.pone.0283746

Cited by 3 publications

(1 citation statement)

References 41 publications

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“…On the other hand, spectral methods have been applied to different types of fractional differential equations. The spectral collocation method [27], as the best spectral method in terms of accuracy, has been applied recently for solving different types of fractional partial differential equations and fractional integro-differential equations [28].…”

Section: Introductionmentioning

confidence: 99%

A Spectral Collocation Method for Solving the Non-Linear Distributed-Order Fractional Bagley–Torvik Differential Equation

Amin,

Abdelkawy,

Solouma

et al. 2023

Fractal Fract

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One of the issues in numerical solution analysis is the non-linear distributed-order fractional Bagley–Torvik differential equation (DO-FBTE) with boundary and initial conditions. We solve the problem by proposing a numerical solution based on the shifted Legendre Gauss–Lobatto (SL-GL) collocation technique. The solution of the DO-FBTE is approximated by a truncated series of shifted Legendre polynomials, and the SL-GL collocation points are employed as interpolation nodes. At the SL-GL quadrature points, the residuals are computed. The DO-FBTE is transformed into a system of algebraic equations that can be solved using any conventional method. A set of numerical examples is used to verify the proposed scheme’s accuracy and compare it to existing findings.

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Section: Introductionmentioning

confidence: 99%

A Spectral Collocation Method for Solving the Non-Linear Distributed-Order Fractional Bagley–Torvik Differential Equation

Amin,

Abdelkawy,

Solouma

et al. 2023

Fractal Fract

Self Cite

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A space-time spectral approximation for solving two dimensional variable-order fractional convection-diffusion equations with nonsmooth solutions

Amin,

Abdelkawy,

Soluma

et al. 2024

Int. J. Mod. Phys. C

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The study focuses on the numerical solutions of two-dimensional variable-order fractional convection-diffusion equations, which combine the principles of diffusion and convection to describe the movement of particles, energy, other physical quantities within a system. The numerical solution is obtained using shifted Legendre Gauss–Lobatto and shifted Chebyshev Gauss–Radau collocation techniques. The convection-diffusion equation is transformed into a system of algebraic equations utilizing shifted Chebyshev Gauss–Radau and shifted Legendre Gauss–Lobatto nodes. Additionally, numerical test examples are presented to demonstrate the method’s efficacy to handle nonsmooth solutions to the given problems.

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Legendre-Gauss-Lobatto collocation method for solving multi-dimensional systems of mixed Volterra-Fredholm integral equations

Amin

Abdelkawy

Amin

et al. 2023

MATH

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<abstract><p>Integral equations play a crucial role in many scientific and engineering problems, though solving them is often challenging. This paper addresses the solution of multi-dimensional systems of mixed Volterra-Fredholm integral equations (SMVF-IEs) by means of a Legendre-Gauss-Lobatto collocation method. The one-dimensional case is addressed first. Afterwards, the method is extended to two-dimensional linear and nonlinear SMVF-IEs. Several numerical examples reveal the effectiveness of the approach and show its superiority in comparison to other alternative techniques for treating SMVF-IEs.</p></abstract>

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Spectral technique with convergence analysis for solving one and two-dimensional mixed Volterra-Fredholm integral equation

Cited by 3 publications

References 41 publications

A Spectral Collocation Method for Solving the Non-Linear Distributed-Order Fractional Bagley–Torvik Differential Equation

A Spectral Collocation Method for Solving the Non-Linear Distributed-Order Fractional Bagley–Torvik Differential Equation

A space-time spectral approximation for solving two dimensional variable-order fractional convection-diffusion equations with nonsmooth solutions

Legendre-Gauss-Lobatto collocation method for solving multi-dimensional systems of mixed Volterra-Fredholm integral equations

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