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High Order Methods for a Class of Volterra Integral Equations with Weakly Singular Kernels [PDF]
, 1974 The solution of the Volterra integral equation, \[ ( * )\qquad x(t) = g_1 (t) + \sqrt {t}g_2 (t) + \int _0^t \frac {K(t,s,x(s))} {\sqrt {t - s} } ds, \quad 0 \leqq t \leqq T,\] where $g_1 (t)$, $g_2 (t)$ and $K(t,s,x)$ are smooth functions, can be ...
de Hoog, Frank, Weiss, Richard
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Attractivity of solutions of Riemann–Liouville fractional differential equations
Electronic Journal of Qualitative Theory of Differential Equations, 2022 Some new weakly singular integral inequalities are established by a new method, which generalize some results of this type in some previous papers.
Tao Zhu
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International Journal of Differential Equations, 2018 An analytical-approximate method is proposed for a type of nonlinear Volterra partial integro-differential equations with a weakly singular kernel. This method is based on the fractional differential transform method (FDTM).
Rezvan Ghoochani-Shirvan +2 more
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Mathematical Modelling and Analysis, 2002 A quadratic spline collocation method for the numerical solution of weakly singular Fredholm integral equations of the second kind and corresponding eigenvalue problem is constructed.
R. Pallav, A. Pedas
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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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Advances in Difference Equations, 2019 This paper investigates some new retarded weakly singular integral inequalities with discontinuous functions for two independent variables. The inequalities given here can be used in the qualitative analysis of various problems for integral equations and
Yaoyao Luo, Run Xu
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Regularized BIE formulations for first- and second-order shape sensitivity of elastic fields. [PDF]
, 1995 The subject of this paper is the formulation of boundary integral equations for first- and second-order shape sensitivities of boundary elastic fields in three-dimensional bodies. Here the direct differentiation approach is considered.
Bonnet, Marc
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Two Singularity Subtraction Schemes for a Class of Nonlinear Weakly Singular Integral Equations
Numerical Functional Analysis and Optimization, 2022 Singularity subtraction for linear weakly singular Fredholm integral equations of the second kind is generalized to nonlinear integral equations. Two approaches are presented: The Classical Ap proach discretizes the nonlinear problem, and uses some finite dimensional linearization process to solve numerically the discrete problem.
Ahues, M. +3 more
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Numerical Treatment of Abel’s Integral Equations Via Chelyshkov Wavelets Collocation Technique [PDF]
Computational Algorithms and Numerical DimensionsThis study presents a method to solve weakly singular Volterra integral equations using an approximation approach. The method relies on Chelyshkov wavelet polynomials. The characteristics of the Chelyshkov wavelet are presented.
Youssef Esmaiel +2 more
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Results in Applied Mathematics, 2023 This paper presents efficient collocation methods for linear Volterra integral equations with weakly singular highly oscillatory kernels. The numerical steepest descent method and generalized Gauss–Laguerre rule are utilized to calculate the weakly ...
Qinghua Wu, Mengjun Sun
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