On Weakly Singular Versions of Discrete Nonlinear Inequalities and Applications [PDF]
Abstract and Applied Analysis, 2014 Some new weakly singular versions of discrete nonlinear inequalities are established, which generalize some existing weakly singular inequalities and can be used in the analysis of nonlinear Volterra type difference equations with weakly singular kernels.
Kelong Cheng, Chunxiang Guo, Qingke Zeng
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Axioms, 2022 This paper is concerned with numerical solutions to Volterra integro-differential equations with weakly singular kernels. Making use of the transformed fractional Jacobi polynomials, we develop a class of piecewise fractional Galerkin methods for solving
Haiyang Li, Junjie Ma
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An efficient spectral method for nonlinear Volterra integro-differential equations with weakly singular kernels [PDF]
Mathematical Modelling and AnalysisFor Volterra integro-differential equations (VIDEs) with weakly singular kernels, their solutions are singular at the initial time. This property brings a great challenge to traditional numerical methods. Here, we investigate the numerical approximation
ZhiPeng Liu, DongYa Tao, Chao Zhang
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Identification of Weakly Singular Relaxation Kernels in Three-Dimensional Viscoelasticity [PDF]
Journal of Mathematical Analysis and Applications, 2001 The author is concerned with the following operator identification problem related to a Hilbert space \(X\), a Banach space \(Y\hookrightarrow X\) (densely) and to a closed subspace \(K\subset {\mathcal L}(X)\): determine a pair of functions \(u:(0,+\infty)\to X\) and \(M:(0,+\infty)\to K\) satisfying the equations \[ u''(t) = Au(t) - \int_0^t M(t-s)Bu(
Janno, Jaan
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Spline quasi-interpolation numerical methods for integro-differential equations with weakly singular kernels [PDF]
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
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Convergence Analysis of Generalized Jacobi-Galerkin Methods for Second Kind Volterra Integral Equations with Weakly Singular Kernels [PDF]
Journal of Function Spaces, 2017 We develop a generalized Jacobi-Galerkin method for second kind Volterra integral equations with weakly singular kernels. In this method, we first introduce some known singular nonpolynomial functions in the approximation space of the conventional Jacobi-
Haotao Cai
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An hp-version discontinuous Galerkin method for integro-differential equations of parabolic type [PDF]
, 2011 We study the numerical solution of a class of parabolic integro-differential equations with weakly singular kernels. We use an $hp$-version discontinuous Galerkin (DG) method for the discretization in time.
H. Mustapha +7 more
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On the Lagrangian Trajectories for the One-Dimensional Euler Alignment Model without Vacuum Velocity
Comptes Rendus. Mathématique, 2020 A well-known result of Carrillo, Choi, Tadmor, and Tan [1] states that the 1D Euler Alignment model with smooth interaction kernels possesses a “critical threshold” criterion for the global existence or finite-time blowup of solutions, depending on the ...
Leslie, Trevor M.
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Minimum-energy measures for singular kernels [PDF]
, 2021 International audienceWe develop algorithms for energy minimization for kernels with singularities. This problem arises in different fields, most notably in the construction of space-filling sequences of points where singularity of kernels guarantees a ...
Pronzato, Luc, Zhigljavsky, Anatoly, A.
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Numerical study of nonlinear problems in the dynamics of thin-walled structural elements [PDF]
E3S Web of Conferences, 2021 Mathematical model of the problem of vibration of thin-walled structural elements has been constructed based on Kirchhoff-Love theory. The problem is reduced, using the Bubnov-Galerkin method, to the solution of a set of nonlinear integro-differential ...
Kucharov Olim +3 more
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