Optimal Homotopy Asymptotic Method for Solving the Linear Fredholm Integral Equations of the First Kind

Almousa, Mohammad; Ismail, Ahmad Izani

doi:10.1155/2013/278097

Cited by 13 publications

(9 citation statements)

References 4 publications

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“…Test examples show that the numerical solution is quite accurate. Almousa and Ismail [91] proposed a semianalytical method, also known as the optimal homotopy (OHAM) asymptotic method, which can be used to solve the numerical solution of the first kind of linear Fredholm integral equation. Three examples are discussed to show the effectiveness of the method.…”

Section: Other Methodsmentioning

confidence: 99%

An overview of numerical methods for the first kind Fredholm integral equation

Zhang

2019

SN Appl. Sci.

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In the field of engineering technology, many problems can be transformed into the first kind Fredholm integral equation, which has a prominent feature called "ill-posedness". This property makes it difficult to find the analytical solution of first kind Fredholm integral equation. Therefore, how to find the numerical solution of first kind Fredholm integral equation has been a common concern of domestic and overseas scholars in recent years. In this article, various numerical solution methods of first kind Fredholm integral equation are introduced in detail. First, the existence and convergence of the solution of the integral equation are given. Second, the current mainstream numerical methods, such as regularization method, wavelet analysis method and multilevel iteration method are introduced in detail. Finally, we presented a concise overview of the numerical method of first kind Fredholm integral equation.

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Section: Other Methodsmentioning

confidence: 99%

An overview of numerical methods for the first kind Fredholm integral equation

Zhang

2019

SN Appl. Sci.

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“…For solving Fredholm-Hammerstein integral equations by using OHAM, we shall follow the approach of [13][14][15][16] and other papers. We rewrite Eq.…”

Section: Anaysis Of the Ohammentioning

confidence: 99%

Numerical solution of Fredholm-Hammerstein integral equations by using optimal homotopy asymptotic method and homotopy perturbation method

Almousa¹,

Ismail²

2014

AIP Conference Proceedings

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“…Khan et al 14 used the proposed method for the solution of first kind Volterra integral equation. Almousa et al 15 applied it for the solution of Fredholm integral equations. Hashmi et al 16 implemented the proposed method for Fredholm integro‐differential equation, and Ghazanfari et al 17 extended it to system of Fredholm integral equations.…”

Section: Introductionmentioning

confidence: 99%

Solutions of system of Volterra integro‐differential equations using optimal homotopy asymptotic method

Agarwal

Akbar

Nawaz

et al. 2020

Math Methods in App Sciences

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In this paper, a powerful semianalytical method known as optimal homotopy asymptotic method (OHAM) has been formulated for the solution of system of Volterra integro‐differential equations. The effectiveness and performance of the proposed technique are verified by different numerical problems in the literature, and the obtained results are compared with Sinc‐collocation method. These results show the reliability and effectiveness of the proposed method. The proposed method does not require discretization like other numerical methods. Moreover, the convergence region can easily be controlled. The use of OHAM is simple and straightforward.

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Optimal Homotopy Asymptotic Method for Solving the Linear Fredholm Integral Equations of the First Kind

Cited by 13 publications

References 4 publications

An overview of numerical methods for the first kind Fredholm integral equation

An overview of numerical methods for the first kind Fredholm integral equation

Numerical solution of Fredholm-Hammerstein integral equations by using optimal homotopy asymptotic method and homotopy perturbation method

Solutions of system of Volterra integro‐differential equations using optimal homotopy asymptotic method

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