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Reproducing kernel method for a class of weakly singular Fredholm integral equations
Journal of Taibah University for Science, 2018 Numerical methods for solving integral equations have been the focus of much research, including reproducing kernel methods. We present a new algorithm to solve weakly singular Fredholm integral equations (WSFIEs). The advantage of this method is that it
Azizallah Alvandi, Mahmoud Paripour
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Singularly perturbed Volterra integral equations with weakly singular kernels [PDF]
International Journal of Mathematics and Mathematical Sciences, 2002 We consider finding asymptotic solutions of the singularly perturbed linear Volterra integral equations with weakly singular kernels. An interesting aspect of these problems is that the discontinuity of the kernel causes layer solutions to decay ...
Angelina Bijura
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Delayed Gronwall inequality with weakly singular kernel
, 2023 Delay Gronwall inequality with a weakly singular kernel has been a subject of interest in various mathematical studies. In this article, we will delve into the consideration of this inequality and its application in the study continuity of the state trajectory for a Volterra integral equation with delay.
Asadzade, Javad A. +2 more
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Fractal and Fractional, 2021 We propose a fractional-order shifted Jacobi–Gauss collocation method for variable-order fractional integro-differential equations with weakly singular kernel (VO-FIDE-WSK) subject to initial conditions.
Mohamed A. Abdelkawy +4 more
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Ain Shams Engineering Journal, 2022 We presented an interpolation method for solving weakly singular Volterra integral equations of the second kind (SVK2). The method based on the barycentric Lagrange interpolation.. For the chosen nodes of the two singular kernel variables, we created two
E.S. Shoukralla +3 more
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A computational method for solving weakly singular Fredholm integral equation in reproducing kernel spaces [PDF]
Iranian Journal of Numerical Analysis and Optimization, 2018 In the present paper, we propose a method to solve a class of weakly singular Fredholm integral equations of the second kind in reproducing kernel spaces.
D. Hamedzadeh, E. Babolian
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Vibrations of dam–plate of a hydro-technical structure under seismic load [PDF]
E3S Web of Conferences, 2021 In present paper, the problem of the vibration of a viscoelastic dam-plate of a hydro-technical structure is investigated, based on the Kirchhoff-Love hypothesis in the geometrically nonlinear statement.
Tukhtaboev A +3 more
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Vibration analysis of airfoil on hereditary deformable suspensions [PDF]
E3S Web of Conferences, 2019 This paper describes the analyses of the nonlinear vibrations and dynamic stability of an airfoil on hereditary-deformable suspensions. The model is based on two-degree-of-freedom structure in geometrically nonlinear statements. It provides justification
Usmonov Botir, Rakhimov Quvvatali
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A Numerical Study for the Dirichlet Problem of the Helmholtz Equation
Mathematics, 2021 In this paper, an effective numerical method for the Dirichlet problem connected with the Helmholtz equation is proposed. We choose a single-layer potential approach to obtain the boundary integral equation with the density function, and then we deal ...
Yao Sun, Shijie Hao
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On the Volterra integral equation with weakly singular kernel [PDF]
Mathematica Bohemica, 2006 Summary: We give sufficient conditions for the existence of at least one integrable solution of equation \(x(t)=f(t)+\int _{0}^{t} K(t,s)g(s,x(s))\,ds\). Our assumptions and proofs are expressed in terms of measures of noncompactness.
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