ADM For Solving Linear Second-Order Fredholm Integro-Differential Equations

Karim, Mohd Fauzihan; Mohamad, Mahathir bin; Rusiman, Mohd Saifullah; Che-Him, Norziha; Roslan, Rozaini; Khalid, Karniza

doi:10.1088/1742-6596/995/1/012009

Cited by 8 publications

(6 citation statements)

References 4 publications

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“…In this section, the effectiveness and accuracy of OHAM is tested by solving Volterra and Fredholm integro-differential equations Problem 1 Consider the Fredhohm integro-differential equation [19] of the following form…”

Section: Implementation Of Oham To Integro-differential Equationsmentioning

confidence: 99%

Optimum Solutions of Fredholm and Volterra Integro-differential Equations

Akbar¹,

Nawaz²,

Ahsan³

2019

IJTAM

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Integro-differential equations arise in modeling various physical and engineering problems. Several numerical and analytical methods have been developed for solving integro-differential equations. In this paper, a powerful semi analytical technique known as Optimal Homotopy Asymptotic Method (OHAM) has been used for finding the approximate solutions of Fredholm type integro-differential equations and Volterra type integro-differential equations. The proposed method does not required discretization like other numerical and approximate method, and it is also free from any small/large parameters. The presented technique provides better accuracy at lower order of approximation, the accuracy of the method can further be increases with higher order of approximation. Moreover, we can easily adjust and control the convergence region. The ability of the method is checked with different problems in literature. The results obtained through OHAM are compared with solutions of Adomian Decomposition Method. It is observed that solutions obtained through the proposed method is more accurate than existing techniques, which proves the validity and stability of the proposed method for solving integrodifferential equations. The presented technique is more consistent, effective, suitable and rapidly convergent. The use of Optimal Homotopy Asymptotic Method is simple and straight forward. For the computation of problems, we have used Mathematica 9.0.

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Section: Implementation Of Oham To Integro-differential Equationsmentioning

confidence: 99%

Optimum Solutions of Fredholm and Volterra Integro-differential Equations

Akbar¹,

Nawaz²,

Ahsan³

2019

IJTAM

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“…Integro-differential equations are equations that are known to emerge in both the derivatives and anti-derivatives of a function [27]. It is an equation in which the unknown function u(x) appears under the integral sign and has yet to be identified [28].…”

Section: Introductionmentioning

confidence: 99%

A New Decomposition Method for Integro-Differential Equations

Olayiwola

Kareem

2022

Cumhuriyet Science Journal

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This present study developed a new Modified Adomian Decomposition Method (MADM) for integro-differential equations. The modification was carried out by decomposing the source term function into series. The terms in the series were then selected in pairs to form the initials for the prevailing approximation. The newly modified Adomian decomposition method (MADM) accelerates the convergence of the solution faster than the Standard Adomian Decomposition Method (SADM). This study recommends the use of the MADM for solving integro-differential equations.

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“…On the other hand, FIDEs are quite difficult to find exact solutions. For this reason, numerical methods play a significant role in this problems, for example, in [5,[8][9][10][11](see, also references therein).…”

Section: Introductionmentioning

confidence: 99%

“…In recent years, there has been a growing interest in the numerical solution of integral equations. The Adomian decomposition method for solving linear second-order FIDEs is presented in [10]. Qing Xue et al [20] studied on an improved reproducing kernel method to find the numerical solution of FIDE type boundary value problems.…”

Section: Introductionmentioning

confidence: 99%

A numerical method for a second order singularly perturbed Fredholm integro-differential equation

Amiraliyev¹,

Durmaz²,

Kudu³

2021

MMN

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The boundary-value problem for a second order singularly perturbed Fredholm integrodifferential equation was considered in this paper. For the numerical solution of this problem, we use an exponentially fitted difference scheme on a uniform mesh which is succeeded by the method of integral identities with the use of exponential basis functions and interpolating quadrature rules with the weight and remainder terms in integral form. Also, the method is first order convergent in the discrete maximum norm. Numerical example shows that recommended method has a good approximation characteristic.

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ADM For Solving Linear Second-Order Fredholm Integro-Differential Equations

Cited by 8 publications

References 4 publications

Optimum Solutions of Fredholm and Volterra Integro-differential Equations

Optimum Solutions of Fredholm and Volterra Integro-differential Equations

A New Decomposition Method for Integro-Differential Equations

A numerical method for a second order singularly perturbed Fredholm integro-differential equation

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