2020
DOI: 10.24996/ijs.2020.61.2.19
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Homotopy Perturbation Method and Convergence Analysis for the Linear Mixed Volterra-Fredholm Integral Equations

Abstract: In this paper, the homotopy perturbation method is presented for solving the second kind linear mixed Volterra-Fredholm integral equations. Then, Aitken method is used to accelerate the convergence. In this method, a series will be constructed whose sum is the solution of the considered integral equation. Convergence of the constructed series is discussed, and its proof is given; the error estimation is also obtained. For more illustration, the method is applied on several examples and programs, which are writ… Show more

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Cited by 4 publications
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“…The accuracy of the approximate solution can also be determined without needing the exact solution, especially in the nonlinear equations [7,9,11]. In recent years, many new methods, such as He's homotopy perturbation method [13,20,21], modified homotopy perturbation method [22], Adomian decomposition method [13,23], variational iteration methods [13,24,25], and many more, were used to solve integral and integro-differential equations. Finally, Al-Hayani [26] combined Laplace transform-Adomian decomposition method to solve nth-order integro-differential equations.…”
Section: Introductionmentioning
confidence: 99%
“…The accuracy of the approximate solution can also be determined without needing the exact solution, especially in the nonlinear equations [7,9,11]. In recent years, many new methods, such as He's homotopy perturbation method [13,20,21], modified homotopy perturbation method [22], Adomian decomposition method [13,23], variational iteration methods [13,24,25], and many more, were used to solve integral and integro-differential equations. Finally, Al-Hayani [26] combined Laplace transform-Adomian decomposition method to solve nth-order integro-differential equations.…”
Section: Introductionmentioning
confidence: 99%