Results 1 to 10 of about 2,673,333 (280)

Fast solvers of weakly singular integral equations of the second kind

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, Arvet Pedas, Gennadi Vainikko   +2 more
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Some new weakly singular integral inequalities and their applications to fractional differential equations

Journal of Inequalities and Applications, 2016
Some new inequalities with weakly singular integral kernel are developed, which generalize some known inequalities and can be used in the qualitative and quantitative analysis of the solutions to certain fractional differential equations.
Run Xu, Fanwei Meng
doaj   +3 more sources

Two‐grid iteration method for weakly singular integral equations

Mathematical Modelling and Analysis, 2000
For the solution of weakly singular integral equations by the piecewise polynomial collocation method it is necessary to solve large linear systems.
K. Hakk
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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
exaly   +3 more sources

Fast and accurate solvers for weakly singular integral equations

Numerical Algorithms, 2022
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Laurence Grammont, Rekha P. Kulkarni, Paulo B. Vasconcelos   +2 more
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Interpolation method for solving Volterra integral equations with weakly singular kernel using an advanced barycentric Lagrange formula

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, B.M. Ahmed, M. Sayed, Ahmed Saeed   +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., Ahues, Mario, Fernandes, Rosario   +2 more
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Explicit bounds of unknown function of some new weakly singular retarded integral inequalities for discontinuous functions and their applications

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
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Sudeshna Banerjea, Barnali Dutta
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