Numerical Solution of the Singular Integral Equations of the First Kind on the Curve

Nadir, Mostefa

doi:10.2478/awutm-2013-0008

“…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. Khairullina and Makletsov [4] studied the solution of SIE by the Wavelet collocation method.…”

Section: Introductionmentioning

confidence: 99%

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

Alhazmi

¹

,

Mahdy

²

,

Abdou

³

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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“…It is known that, the most effective methods for the approximate solution of weakly singular integrodifferential equations consists in their reduction to a system of linear algebraic equations by the replacement of the integral with a proper quadrature sum [5][6][7].…”

Section: Introductionmentioning

confidence: 99%

A new technical for solving a weakly singular integro-differential equations

Nadir¹

2017

Journal of Taibah University for Science

Self Cite

1

0

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“…It is known that, the most effective methods for the approximate solution of weakly singular integrodifferential equations consists in their reduction to a system of linear algebraic equations by the replacement of the integral with a proper quadrature sum [5,6,7].…”

Section: Introductionmentioning

confidence: 99%

“…where Γ designates a smooth-oriented contour; t and t 0 are points on Γ and f (t) is a given function on Γ, the density ϕ(t) is the desired function has to satisfy the Holder condition H(µ) [6].…”

Section: Introductionmentioning

confidence: 99%