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

Almousa, Mohammad; Ismail, Ahmad Izani

doi:10.1063/1.4887570

Cited by 5 publications

(3 citation statements)

References 11 publications

(12 reference statements)

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“…Consider the following coupled system composed of third and second nonlinear equations, with three-point boundary conditions: 2 (sin(u 1 (t)u 2 (t)) + 1), u(0) = u (0) = 0, u (1) = 3 2 u ( 1 2 ), v(0) = 0, v (1) = 3 2 v ( 1 2 ).…”

Section: Examplementioning

confidence: 99%

Coupled systems of Hammerstein integral equations

2022

Trends in Abstract and Applied Analysis

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In this paper we deal with generalized coupled systems of integral equations of Hammerstein type with nonlinearities depending on several derivatives of both variables and we underline that both equations and both variables can have a different regularity. This detail is very important as it allows for the application to, for example, boundary value problems with coupled systems composed of differential equations of different orders and distinct boundary conditions. This issue will open a new field of applications to phenomena modeled by coupled systems requiring different types of regularity for the unknown functions.The arguments follow Guo-Krasnosel'skiȋ compression-expansion theory on cones and the kernel functions are nonnegative and verifying adequate sign and growth assumptions.The dependence of the derivatives is overcome by the construction of suitable cones taking into account certain conditions of sublinearity/superlinearity at the origin and at +∞.

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Section: Examplementioning

confidence: 99%

Coupled systems of Hammerstein integral equations

2022

Trends in Abstract and Applied Analysis

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“…-u 1 (t) = (t 2 + 1)(e -(u 2 (t)+u 1 (t)) 2 + |u 1 (t) + u 2 (t)|), u 2 (t) = t 4 (2 + cos(u 2 (t) + u 1 (t)) 2 (sin(u 1 (t)u 2 (t)) + 1), u(0) = u (0) = 0, u (1) = 3 2 u ( 1 2 ), v(0) = 0, v (1) = 3 2 v ( 1 2 ).…”

Section: Examplementioning

confidence: 99%

On coupled systems of Hammerstein integral equations

Sousa¹,

Minhós²

2019

Bound Value Probl

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In this paper we deal with generalized coupled systems of integral equations of Hammerstein type with nonlinearities depending on several derivatives of both variables and we underline that both equations and both variables can have a different regularity. This detail is very important as it allows for the application to, for example, boundary value problems with coupled systems composed of differential equations of different orders and distinct boundary conditions. This issue will open a new field of applications to phenomena modeled by coupled systems requiring different types of regularity for the unknown functions. The arguments follow Guo-Krasnosel'skiȋ compression-expansion theory on cones and the kernel functions are nonnegative and verifying adequate sign and growth assumptions. The dependence of the derivatives is overcome by the construction of suitable cones taking into account certain conditions of sublinearity/superlinearity at the origin and at +∞.

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“…This method is modified to improve the accuracy of the results. (See [10], [11], [12], [13], [14], [15]).…”

Section: Introductionmentioning

confidence: 99%

A Hybrid Laplace Transform-Optimal Homotopy Asymptotic Method (LT-OHAM) for Solving Integro-Differential Equations of the Second Kind

Almousa,

Al-Hammouri,

Saidat

et al. 2024

Int. J. Anal. Appl.

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The new proposed hybrid method between optimal homotopy asymptotic method and Laplace transform namely LT-OHAM is formulated for the first time in our paper. This hybrid method presents significant features of LT-OHAM and its capability of handling IDEs. This formulation is developed to find the solution of IDEs. By using the new presented hybrid method, some applications of IDEs are solved. This hybrid method seems very efficient and easy to solve these types of equations.

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

Cited by 5 publications

References 11 publications

Coupled systems of Hammerstein integral equations

Coupled systems of Hammerstein integral equations

On coupled systems of Hammerstein integral equations

A Hybrid Laplace Transform-Optimal Homotopy Asymptotic Method (LT-OHAM) for Solving Integro-Differential Equations of the Second Kind

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