An Asymptotic Model for Solving Mixed Integral Equation in Position and Time

Jan, A. R.

doi:10.1155/2022/8063971

Cited by 9 publications

(6 citation statements)

References 22 publications

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“…To proof EUS of Equation (1.1) we utilize BFP theorem or Picard technique. The author of [21] used Picard technique. In this paper we use BFP assumption to proof the EUS of Equation (1.1).…”

Section: Existence Of a Unique Solution Of Mv-fiementioning

confidence: 99%

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A computational technique for computing second-type mixed integral equations with singular kernels

Mahdy,

Abdou,

Mohamed

2023

J. Math. Computer Sci.

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In the present article, we establish the numerical solution for the mixed Volterra-Fredholm integral equation (MV-FIE) and it has a discontinuous kernel in position. While the Volterra integral term is considered in the class of time C[0, T ], T < 1, and has a continuous kernel in time. The necessary conditions have been established to ensure that there is a single solution in the space L 2 [−1, 1] × C[0, T ], T < 1. By utilizing the separation of variables technique, MV-FIE is transformed to Fredholm integral equation (FIE) of the second kind with variables coefficients in time. The separation technique of variables helps the authors choose the appropriate time function to establish the conditions of convergence in solving the problem and obtaining its solution. Then, using the Boubaker polynomials method, we end up with a linear algebraic system (LAS) abbreviated. The Banach fixed point (BFP) hypothesis has been presented to determine the existence and uniqueness of the solution of the LAS. The convergence of the solution and the stability of the error are discussed. The Maple 18 software is used to perform some numerical calculations once some numerical experiments have been taken into consideration.

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Section: Existence Of a Unique Solution Of Mv-fiementioning

confidence: 99%

“…. In the first example we consider MV-FIE with weakly singular kernel, a comparison was made between the Boubaker method and Toeplitz matrix method which is used in[21] in Table1, at the…”

mentioning

confidence: 99%

A computational technique for computing second-type mixed integral equations with singular kernels

Mahdy,

Abdou,

Mohamed

2023

J. Math. Computer Sci.

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“…In the sense that the problem is caused by an elastic plate with a curved opening in the complex an edge crack isotropic plate under different loadings. The works of Duruk et al [5], Jan [6], and plane of the theory of elasticity, there are two possible solutions: the first is to move the curved opening outside the unit circle. Exadaktylos et al…”

Section: Introductionmentioning

confidence: 99%

Untitled

2024

appl. Math. Inf. Sci.

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This paper reports on a new study of a flexible plate reduced by a curvilinear slot with the cavity transported conformally to the right half-plane with complex constant parameters of the rational mapping function. Some figures of the conformal mapping for different values of complex constants were also obtained. Some special and important cases have been derived. Also, a closed form of the two Gaursat functions was derived using the complex variable method for the first and second fundamental problems. This is done by converting the first and second basic equations, in the presence of heat, into an integral differential equation in the right half plane with a Cauchy kernel. In addition, the researcher was able to discuss some important applications while studying the effect of temperature in each case. All calculations and computations of various stress components for each application are performed using the Maple 18 program. This study differs from previously published literature, which had areas mapped identically outside or inside the unit circle.

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“…In the late twenty-first century, some authors began to study the effect of the time function in solving all kinds of integral equations (IEs). For more information, see [29][30][31][32]. Three-dimensional MVFIEs are solved computationally by Mahdy et al,in [33].…”

Section: Introductionmentioning

confidence: 99%

Computational Methods for Solving Higher-Order (1+1) Dimensional Mixed-Difference Integro-Differential Equations with Variable Coefficients

2023

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The main purpose of this article is to present a new technique for solving (1+1) mixeddimensional difference integro-differential Equations (2D-MDeIDEs) in position and time with coefficients of variables under mixed conditions. The equations proposed for the solution represent a link between time and delay in position that has not been previously studied. Therefore, the authors used the technique of separation of variables to transform the 2D-MDeIDE into one-dimensional Fredholm difference integro-differential Equations (FDeIDEs), and then using the Bernoulli polynomial method (BPM), we obtained a system of linear algebraic equations (SLAE). The other aspect of the technique of separation of variables is explicitly obtaining the necessary and appropriate time function to obtain the best numerical results. Some numerical experiments are performed to show the simplicity and efficiency of the presented method, and all results are performed by Maple 18.

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An Asymptotic Model for Solving Mixed Integral Equation in Position and Time

Abstract: In this paper, we considered a mixed integral equation (MIE) of the second kind in the space L 2 − b , … Show more

Cited by 9 publications

References 22 publications

A computational technique for computing second-type mixed integral equations with singular kernels

A computational technique for computing second-type mixed integral equations with singular kernels

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Computational Methods for Solving Higher-Order (1+1) Dimensional Mixed-Difference Integro-Differential Equations with Variable Coefficients

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