Periodic Solution of Integro-Differential Equations Depended on Special Functions with Singular Kernels and Boundary Integral Conditions

Butris, Raad N.

doi:10.30534/ijatcse/2019/73842019

Cited by 3 publications

(3 citation statements)

References 4 publications

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“…We consider the numerical implementation of finitedifference computations for simplicity in the twodimensional case [6][7][8][9][10][11].and which illustrates the exact solution, forward modeling and migration [12][13][14][15][16][17]. Let the model be given on a regular rectangular grid with nodes   , i j .…”

Section: Approximation and Convergencementioning

confidence: 99%

Numerical simulation of the acoustic wave equation by the method of reverse time migration

2020

IJATCSE

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The paper deals with seismic method of studying the structure of the earth crust namely reverse time migration (RTM) [1]. Migration is described by a conventional wave equation and is performed by propagating the data down through the acoustic pressure to the ground and it is constrained where the structure and acoustic pressure field generate more complex arrivals, such as turn waves and prisms. Since the wave pressure is variable in the earth interior, this wave equation has different coefficients [2]. Also, this paper discusses the existence and uniqueness of solutions of partial differential equations using Fourier transform [3]. Linearization is used for finding approximate solutions, which is direct problem. This model is used in the migration method to construct an image of reflecting boundaries. In addition, in this paper we study the solution of inverse problems of the wave equation allowing the study of the characteristics of the earth underground medium.

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Section: Approximation and Convergencementioning

confidence: 99%

Numerical simulation of the acoustic wave equation by the method of reverse time migration

2020

IJATCSE

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“…B ut in industrial problems we have not spatial cases so that we try to solve this kind of equations numerically in general format. Many numerical schemes are employed to give an approximate solution with sufficient accuracy [3,4,6,7,8,9,10].…”

Section: Introductionmentioning

confidence: 99%

Some Results in the Existence, Uniqueness and Stability Periodic Solution of New Volterra Integral Equations With Singular Kernel

Butris

2020

IJISCS

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The aim of this work is to study the existence, uniqueness and stability of periodic solutions of some classes for non-linear systems of new Volterra integral equations with singular kernel in two variables by using Riemann integrals. Furthermore, we investigation the existence, uniqueness and stability of the fundamental tools employed in the analysis are based on applications by depending on the numerical-analytic method for studying the periodic solutions of ordinary differential equations which were introduced by Samoilenko.The study of such nonlinear Volterra integral equations with singular kernel leads us to improve and extend Samoilenko method. Thus the non-linear integral equations with singular kernel that we have introduced in the study become more general and detailed than those introduced by Butris .

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“…In the original works of Samoilenk and Ronto [16,17 ] the approach used and described here had been referred to as the numericalanalytic based upon successive approximations. The idea of the method, originally aimed at the investigation of periodic solution only, had been later applied in studies [2,3,8,9,10,11,13,14,15]. Also, it should be noted that appropriate versions of the method considered can be applied in many situations for handling periodic in the cases of the systems of first or second order ordinary differential equations, integrodifferential equations, equations with retarded arguments, systems containing unknown parameters, and countable systems of differential equations.…”

Section: Introductionmentioning

confidence: 99%

Periodic solutions for nonlinear systems of integro-differential equations of Volterra- Friedholm type

Butris¹

2019

IJATCSE

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In this work, we study the periodic solutions for nonlinear systems of integro-differential equations of Volterra-Friedholm. The numerical analytic method has been used by (Samoilenko A. M.) to investigate the existence and approximation of periodic solutions for certain of nonlinear systems of integro-differential equations. Also these methods could be developed and extended throughout the study.

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Periodic Solution of Integro-Differential Equations Depended on Special Functions with Singular Kernels and Boundary Integral Conditions

Cited by 3 publications

References 4 publications

Numerical simulation of the acoustic wave equation by the method of reverse time migration

Numerical simulation of the acoustic wave equation by the method of reverse time migration

Some Results in the Existence, Uniqueness and Stability Periodic Solution of New Volterra Integral Equations With Singular Kernel

Periodic solutions for nonlinear systems of integro-differential equations of Volterra- Friedholm type

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