Results 11 to 20 of about 16,231 (283)
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
doaj +2 more sources
Journal of Mathematics, 2022 In this paper, we propose and analyze a spectral approximation for the numerical solutions of fractional integro-differential equations with weakly kernels.
Xiulian Shi
doaj +2 more sources
A generalized Chebyshev operational method for Volterra integro-partial differential equations with weakly singular kernels [PDF]
HeliyonVolterra integro-partial differential equations with weakly singular kernels (VIPDEWSK) are utilized to model diverse physical phenomena. A matrix collocation method is proposed for determining the approximate solution of this functional equation ...
Khadijeh Sadri +4 more
doaj +2 more sources
A Hybrid Collocation Method for Volterra Integral Equations with Weakly Singular Kernels [PDF]
SIAM Journal on Numerical Analysis, 2003 This paper presents a new hybrid collocation method for solving certain second kind Volterra integral equations with singular kernels. The solution of the equation has a singularity, caused by the singularity in the kernel, and this presents particular challenges for numerical schemes.
Cao, Y. Z., Herdman, Terry L., Xu, Y. H.
openaire +4 more sources
Mathematical Modelling and AnalysisIn this work, we introduce a numerical approach that utilizes spline quasi-interpolation operators over a bounded interval. This method is designed to provide a numerical solution for a class of Fredholm integro-differential equations with weakly ...
Abdelmonaim Saou +3 more
doaj +4 more sources
Mathematical Modelling and Analysis, 2009 We propose a piecewise polynomial collocation method for solving linear Volterra integral equations of the second kind with kernels which, in addition to a weak diagonal singularity, may have a weak boundary singularity.
Marek Kolk, Arvet Pedas
doaj +4 more sources
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
doaj +1 more source
Journal of Mathematics, 2022 In this paper, a new approach for solving the system of fractional integro-differential equation with weakly singular kernels is introduced. The method is based on a class of symmetric orthogonal polynomials called shifted sixth-kind Chebyshev ...
S. Yaghoubi, H. Aminikhah, K. Sadri
doaj +1 more source
Fractal and Fractional, 2021 We consider general linear multi-term Caputo fractional integro-differential equations with weakly singular kernels subject to local or non-local boundary conditions.
Arvet Pedas, Mikk Vikerpuur
doaj +1 more source
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
openaire +2 more sources