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Fast solvers of weakly singular integral equations of the second kind [PDF]
Mathematical Modelling and Analysis, 2018 We discuss the bounds of fast solving weakly singular Fredholm integral equations of the second kind with a possible diagonal singularity of the kernel and certain boundary singularities of the derivatives of the free term when the information about the ...
Sumaira Rehman +2 more
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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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Some Weakly Singular Integral Inequalities and Their Applications to Tempered Fractional Differential Equations [PDF]
Journal of Mathematics, 2022 In this paper, we establish several new weakly singular integral inequalities that generalize several previously known ones. Several applications for fractional differential equations in the Caputo context have been derived using tempered fractional ...
Abdellatif Ben Makhlouf +3 more
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Tau approximate solution of weakly singular Volterra integral equations
Mathematical and Computer Modelling, 2013 Abstract In this paper, we present a numerical solution of weakly singular Volterra integral equations including the Abel’s equations by the Tau method with arbitrary polynomial bases. The Tau method produces approximate polynomial solutions of differential, integral and integro-differential equations. An extension of the Tau method has been done for
Fazlollah Soleymani, S Karimi Vanani
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Fast and accurate solvers for weakly singular integral equations
Numerical Algorithms, 2022 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Laurence Grammont +2 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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ERRORS AND GRIDS FOR PROJECTED WEAKLY SINGULAR INTEGRAL EQUATIONS [PDF]
International Journal of Pure and Apllied Mathematics, 2013 Summary: In the solution of weakly singular Fredholm integral equations of the second kind defined on the space of Lebesgue integrable complex valued functions by projection methods, the choice of the grid is crucial. We will present the proof of an error bound in terms of the mesh size of the underlying discretization grid on which no regularity ...
d'Almeida, Filomena, D. +2 more
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Journal of Inequalities and Applications, 2017 The purpose of the present paper is to establish some new retarded weakly singular integral inequalities of Gronwall-Bellman type for discontinuous functions, which generalize some known weakly singular and impulsive integral inequalities.
Zizun Li, Wu-Sheng Wang
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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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On a weakly singular integral equation and its application
Applied Mathematics Letters, 2008 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Sudeshna Banerjea, Barnali Dutta
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