Numerical treatments for solving nonlinear mixed integral equation

Abdou, M. A.; Basseem, M.

doi:10.1016/j.aej.2016.02.035

Cited by 2 publications

(3 citation statements)

References 10 publications

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“…Among these are optimal homotopy asymptotic method [1,2], homotopy perturbation method [3,4], homotopy analysis method [5], Adomian Decomposition Method [6], barycentric interpolation collocation methods [7], quadrature method based on multivariate Bernstein polynomials [8], integral mean value theorem [9] and Newton-Kantorovich-quadrature method [10]. Other studies can be found on [11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

Adomian Decomposition Method with Modified Bernstein Polynomials for Solving Nonlinear Fredholm and Volterra Integral Equations

Almousa¹

2020

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Many different problems in mathematics, physics, engineering can be expressed in the form of integral equations. Among these are diffraction problems, population growth, heat transfer, particle transport problems, electrical engineering, elasticity, control, elastic waves, diffusion problems, quantum mechanics, heat radiation, electrostatics and contact problems. Therefore, the solutions which are obtained by the mathematical methods play an important role in these fields. The most two basic types of integral equations are called Fredholm (FIEs) and Volterra (VIEs). In many instances, the ordinary and partial differential equations can be converted into Fredhom and Volterra integral equations that are solved more effectively. We aim through this research to present an improved Adomian decomposition method based on modified Bernstein polynomials (ADM-MBP) to solve nonlinear integral equations of the second kind. We introduced efficient method, constructed on modified Bernstein polynomials. The formulation is developed to solve nonlinear Fredholm and Volterra integral equations of second kind. This method is tested for some examples from nonlinear integral equations. Maple software was used to obtain the solutions of these examples. The results demonstrate reliability of the proposed method. Generally, the proposed method is very convenient to apply to find the solutions of Fredholm and Volterra integral equations of second kind.

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Section: Introductionmentioning

confidence: 99%

Adomian Decomposition Method with Modified Bernstein Polynomials for Solving Nonlinear Fredholm and Volterra Integral Equations

Almousa¹

2020

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“…The existence and uniqueness of the solution, under certain conditions, are discussed in the space L 2 [0, 1] × C n [0, T ], 0 ≤ T < 1. We use a numerical method to transform the Fredholm-Volterra integral equations to a linear system of Fredholm integral equations [2,9].…”

Section: Introductionmentioning

confidence: 99%

“…The equation (2) with initial condition (3) is called Integro-Differential Equation for the Phase-Lag. The Integro-Differential Equation is a kind of functional equation that has associate integral and derivatives of unknown function.…”

Section: Introductionmentioning

confidence: 99%

Study of the normality and continuity for the mixed integral equations with phase-lag term

Abdou¹,

Nasr²,

Abdel–Aty³

2017

ijma

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In this paper, the existence and uniqueness solution of the Fredholm-Volterra integral equations (F-VIEs) are considered in the space L 2 [0, 1]× C n [0, T ], 0 ≤ T < 1. Using a numerical technique, F-VIEs lead to a system of linear Fredholm integral equations (SLFIEs). Also, the normality and the continuity of integral operator are discussed. The Trapezoidal Rule is used to get the solution of SLFIEs. Finally, numerical results are discussed and the error estimate is computed.

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Numerical treatments for solving nonlinear mixed integral equation

Cited by 2 publications

References 10 publications

Adomian Decomposition Method with Modified Bernstein Polynomials for Solving Nonlinear Fredholm and Volterra Integral Equations

Adomian Decomposition Method with Modified Bernstein Polynomials for Solving Nonlinear Fredholm and Volterra Integral Equations

Study of the normality and continuity for the mixed integral equations with phase-lag term

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