Collocation approximations for weakly singular Volterra integro‐differential equations
Mathematical Modelling and Analysis, 2003 A piecewise polynomial collocation method for solving linear weakly singular integro‐differential equations of Volterra type is constructed. The attainable order of convergence of collocation approximations on arbitrary and quasi‐uniform grids is studied
I. Parts, A. Pedas
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MathematicsThis work aims to propose an iterative method for approximating solutions of two-dimensional weakly singular Fredholm integral Equation (2D-WSFIE) by incorporating the product integration technique, an appropriate cubature formula, and the Picard ...
Mohamed I. Youssef +2 more
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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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Singularly perturbed Volterra integral equations with weakly singular kernels
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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analysis of Product Integration Methods for a Class of Singular Volterra Integral Equations
Trends in Computational and Applied Mathematics, 2000 The construction and analysis of high order numerical methods for Volterra integral equations with a certain weakly singular kernel have been investigated in [6], under the assumption the the solution is sufficiently smooth.
T. Diogo, P. Lima, N.B. Franco
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Numerical Solution of Integral-Algebraic Equations with Weakly Singular Kernels by k−step Methods
Известия Иркутского государственного университета: Серия "Математика", 2015 In this paper we describe numerical methods for solution integral-algebraic equations wiht weakly singular kernels. Methods are based on explicit Adam’s methods, product integration methods for the integral part and on extrapolation formulas for the main
M.V. Bulatov, O.S. Budnikova
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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
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Numerical quadrature methods for integrals of singular periodic functions and their application to singular and weakly singular integral equations [PDF]
High accuracy numerical quadrature methods for integrals of singular periodic functions are proposed. These methods are based on the appropriate Euler-Maclaurin expansions of trapezoidal rule approximations and their extrapolations.
Israeli, M., Sidi, A.
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Generalized nonlinear weakly singular retarded integral inequalities with maxima and their applications. [PDF]
J Inequal Appl, 2018 Yan Y, Zhou D, Zhao J.
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Optimal convergence for adaptive IGA boundary element methods for weakly-singular integral equations. [PDF]
Numer Math (Heidelb), 2017 Feischl M +3 more
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