Numerical solution of two-dimensional Fredholm integro-differential equations by Chebyshev integral operational matrix method

Ishola, Christie Yemisi; Taiwo, Omotayo Adebayo; Adebisi, A. F.; Peter, Olumuyiwa James

doi:10.17512/jamcm.2022.1.03

Cited by 5 publications

(2 citation statements)

References 12 publications

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“…These include fractional order derivatives [7,27]. The mathematical model equations can also be discretized using other base polynomials such as ones based upon Chebyshev polynomials or integrals [1,21]. Recently, HBV has been the important focus of authors and researchers to capture the Caputo type fractional operator [10,13].…”

Section: Introductionmentioning

confidence: 99%

Perturbation Iteration Method Compared with Direct Method and Fuzzy Logic Strategy for Solving An Optimal Control Problem of An Uninfected Hepatitis B Virus Dynamics

Mahamat Saleh,

Ntaganda

2023

MJMS

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This paper aims at solving the optimal control problem of the dynamic of HBV infection under treatment using the perturbation iteration method. This method serves as a tool to determine the approximate solutions of nonlinear equations for which exact solutions cannot be obtained. To test the efficacy of this method, the authors propose to compare the numerical simulation results with those of the direct method and fuzzy logic strategy. The newly used method for solving the above optimal control problem is very important since the findings compared to those obtained from the two other methods are in good agreement with experimental data and they demonstrate the response drugs to the dynamics of uninfected hepatocytes, infected hepatocytes, and free virions for a patient suffering from HBV. Since the perturbation iteration method provides satisfactory results which are close to other used numerical methods, it is an important numerical tool to determine the solution of an optimal control problem. In particular, it provides optimal trajectories in medicine, biology, and other related scientific fields. For instance, the response of treatment as control of the human body ensures the health of patients.

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Section: Introductionmentioning

confidence: 99%

Perturbation Iteration Method Compared with Direct Method and Fuzzy Logic Strategy for Solving An Optimal Control Problem of An Uninfected Hepatitis B Virus Dynamics

Mahamat Saleh,

Ntaganda

2023

MJMS

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“…Other studies with different approch for solving integro-diffrential equations can be found in [17][18][19][20][21][22] In this work, Akbari-Ganji's Method (AGM) is proposed for the solution of Volterra Integro-Differential Difference Equations (VIDDE). The approach of [14] is followed.…”

Section: Introductionmentioning

confidence: 99%

Numerical Solution of Volterra Integro-Differential Equations by Akbari-Ganji’s Method

Uwaheren

Adebisi

Ishola

et al. 2022

BAREKENG: J. Math. & App.

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In this study, Akbari-Ganji’s Method (AGM) was applied to solve Volterra Integro-Differential Difference Equations (VIDDE) using Legendre polynomials as basis functions. Here, a trial solution function of unknown constants that conform with the differential equations together with the initial conditions were assumed and substituted into the equations under consideration. The unknown coefficients are solved for using the new proposed approach, AGM which principally involves the application of the boundary conditions on successive derivatives and integrals of the problem to obtain a system of equations. The system of equation is solved using any appropriate computer software, Maple 18. Some examples were solved and the results compared to the exact solutions.

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Numerical solution of Volterra–Fredholm integral equation systems by operational matrices of integration based on Bernstein multi-scaling polynomials

Yaghoobnia

Ezzati

2022

Comp. Appl. Math.

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Numerical solution of two-dimensional Fredholm integro-differential equations by Chebyshev integral operational matrix method

Cited by 5 publications

References 12 publications

Perturbation Iteration Method Compared with Direct Method and Fuzzy Logic Strategy for Solving An Optimal Control Problem of An Uninfected Hepatitis B Virus Dynamics

Perturbation Iteration Method Compared with Direct Method and Fuzzy Logic Strategy for Solving An Optimal Control Problem of An Uninfected Hepatitis B Virus Dynamics

Numerical Solution of Volterra Integro-Differential Equations by Akbari-Ganji’s Method

Numerical solution of Volterra–Fredholm integral equation systems by operational matrices of integration based on Bernstein multi-scaling polynomials

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