A Novel Method for Solving Second Kind Volterra Integral Equations with Discontinuous Kernel

Noeiaghdam, Samad; Micula, Sanda

doi:10.3390/math9172172

Cited by 10 publications

(2 citation statements)

References 41 publications

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“…Jafarian et al [1] used the Bernstein polynomials technique for solving Abel integral equations. A unique approach to solving second-kind Volterra integral equations with discontinuous kernels is presented by Noeiaghdam and Micula in their paper [2]. Nadir [3] applied a quadratic technique for solving SIE of the first kind.…”

Section: Introductionmentioning

confidence: 99%

Computational Techniques for Solving Mixed (1 + 1) Dimensional Integral Equations with Strongly Symmetric Singular Kernel

et al. 2023

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This paper describes an effective strategy based on Lerch polynomial method for solving mixed integral equations (MIE) in position and time with a strongly symmetric singular kernel in the space L2(−1,1)×C[0,T],(T<1). The Quadratic numerical method (QNM) was applied to obtain a system of Fredholm integral equations (SFIE), then the Lerch polynomials method (LPM) was applied to transform SFIE into a system of linear algebraic equations (SLAE). The existence and uniqueness of the integral equation’s solution are discussed using Banach’s fixed point theory. Also, the convergence and stability of the solution and the stability of the error are discussed. Several examples are given to illustrate the applicability of the presented method. The Maple program obtains all the results. A numerical simulation is carried out to determine the efficacy of the methodology, and the results are given in symmetrical forms. From the numerical results, it is noted that there is a symmetry utterly identical to the kernel used when replacing each x with y.

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Section: Introductionmentioning

confidence: 99%

Computational Techniques for Solving Mixed (1 + 1) Dimensional Integral Equations with Strongly Symmetric Singular Kernel

et al. 2023

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“…Providas [36] discussed the analytical and numerical methods for solving FIE. In [34], Noeiaghdam and Micula used Lagrangecollocation method for solving VIE with discontinuous kernel.…”

Section: Introductionmentioning

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 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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Solving generalized nonlinear functional integral equations with applications to epidemic models

Halder,

Vandana,

Deepmala

2024

Math Methods in App Sciences

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In this article, we investigate the existence and uniqueness of solutions to a generalized nonlinear functional integral equation (G‐NLFIE) associated with certain epidemic models of infectious diseases, defined within the Banach space . Our existence results include several specific cases of nonlinear functional integral equations that commonly occur in nonlinear sciences. We then introduce an iterative algorithm that combines Adomian's decomposition method (ADM) with the modified homotopy perturbation method (mHPM) to approximate solutions to the G‐NLFIE. The paper addresses the convergence properties and error analysis of this method. Finally, we present numerical examples to demonstrate the effectiveness and efficiency of our proposed approach.

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A Novel Method for Solving Second Kind Volterra Integral Equations with Discontinuous Kernel

Cited by 10 publications

References 41 publications

Computational Techniques for Solving Mixed (1 + 1) Dimensional Integral Equations with Strongly Symmetric Singular Kernel

Computational Techniques for Solving Mixed (1 + 1) Dimensional Integral Equations with Strongly Symmetric Singular Kernel

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

Solving generalized nonlinear functional integral equations with applications to epidemic models

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