Relevant bibliographies by topics / Weakly singular kernel

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters
  4. Conference papers
  5. Reports

Academic literature on the topic 'Weakly singular kernel'

Author: Grafiati
Published: 4 June 2021
Last updated: 25 July 2025

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Journal articles on the topic "Weakly singular kernel"

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Usmonov, Botir. "A Numerical Solution of Hereditary Equations with a Weakly Singular Kernel for Vibration Analysis of Viscoelastic Systems / Vienâdojumu Ar Vâjo Singulâro Kodolu Skaitliskais Risinâjums Iedzimto Viskoelastîgo Sistçmu Vibrâciju Analîzei." Proceedings of the Latvian Academy of Sciences. Section B. Natural, Exact, and Applied Sciences. 69, no. 6 (2015): 326–30. http://dx.doi.org/10.1515/prolas-2015-0048.

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Abstract Viscoelastic, or composite materials that are hereditary deformable, have been characterised by exponential and weakly singular kernels in a hereditary equation. An exponential kernel is easy to be numerically implemented, but does not well describe complex vibratory behaviour of a hereditary deformable system. On the other hand, a weakly singular kernel is known to describe the complex vibratory behaviour, but is nontrivial to be numerically implemented. This study presents a numerical formulation for solving a hereditary equation with a weakly singular kernel. Recursive algebraic eq
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Bijura, Angelina. "Singularly perturbed Volterra integral equations with weakly singular kernels." International Journal of Mathematics and Mathematical Sciences 30, no. 3 (2002): 129–43. http://dx.doi.org/10.1155/s016117120201325x.

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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 algebraically rather than exponentially within the initial (boundary) layer. To analyse this phenomenon, the paper demonstrates the similarity that these solutions have to a special function called the Mittag-Leffler function.
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Szufla, Stanisław. "On the Volterra integral equation with weakly singular kernel." Mathematica Bohemica 131, no. 3 (2006): 225–31. http://dx.doi.org/10.21136/mb.2006.134139.

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Darania, Parviz, Bahaa Hussain Alrikabi, and Saeed Pishbin. "Development of the Nystr\"{o}m Method for Weakly Singular Functional Integral Equations." European Journal of Pure and Applied Mathematics 18, no. 2 (2025): 5704. https://doi.org/10.29020/nybg.ejpam.v18i2.5704.

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In this research, we apply the standard product integration method (Nystr\"{o}m method) for solving the delay nonlinear weakly singular Volterra integral equations. Typically, in weakly singular integral equations, the singularity of the kernel leads to the derivatives of the solution becoming singular at the boundary of the domain. The Chelyshkov polynomials serving as orthogonal polynomials, find application in numerical integration. Here, we use roots of these polynomials to make Lagrange interpolating polynomial for approximating the kernel functions in weakly singular functional integral
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Zheng, Kelong, Wenqiang Feng, and Chunxiang Guo. "Some New Nonlinear Weakly Singular Inequalities and Applications to Volterra-Type Difference Equation." Abstract and Applied Analysis 2013 (2013): 1–6. http://dx.doi.org/10.1155/2013/912874.

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Some new nonlinear weakly singular difference inequalities are discussed, which generalize some known weakly singular inequalities and can be used in the analysis of nonlinear Volterra-type difference equations with weakly singular kernel. An application to the upper bound of solutions of a nonlinear difference equation is also presented.
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Dhunde, Ranjit R. "Double Laplace Transform Method for Solving Fractional Fourth-Order Partial Integro-Differential Equations with Weakly Singular Kernel." Indian Journal Of Science And Technology 17, no. 36 (2024): 3712–18. http://dx.doi.org/10.17485/ijst/v17i36.2005.

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Objectives: To investigates the solutions of fourth order partial integro-differential equations with high-order non-integer derivatives and weakly singular kernels. Methods: Weakly singular kernels present challenges in both analytical and numerical treatments due to their intricate behaviour near singular points. In this article, we introduce a novel approach utilizing the double Laplace transform method to effectively address these challenges. Findings: By solving a series of precise and understandable examples, the double Laplace transform clearly transforms the fractional partial integro-
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Bazine, Imane, and Samir Lemita. "Fredholm integro-differential equation with weak singularities: a combined analytical and numerical study." STUDIES IN ENGINEERING AND EXACT SCIENCES 5, no. 2 (2024): e9901. http://dx.doi.org/10.54021/seesv5n2-413.

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This study is dedicated to the analytical and numerical investigation of a nonlinear Fredholm integro-differential equation, specifically one that is characterized by weakly singular kernels. The primary challenge addressed is the weak singularity in the kernel, which complicates the solution process. To tackle this, we employ a combination of two techniques: the Nyström method and the product integration method. The Nyström method is used for approximating the solution to the Fredholm integro-differential equation, while the product integration technique is applied to handle the singular beha
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Gao, Jing, and Yao-Lin Jiang. "A periodic wavelet method for the second kind of the logarithmic integral equation." Bulletin of the Australian Mathematical Society 76, no. 3 (2007): 321–36. http://dx.doi.org/10.1017/s0004972700039721.

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A periodic wavelet Galerkin method is presented in this paper to solve a weakly singular integral equations with emphasis on the second kind of Fredholm integral equations. The kernel function, which includes of a smooth part and a log weakly singular part, is discretised by the periodic Daubechies wavelets. The wavelet compression strategy and the hyperbolic cross approximation technique are used to approximate the weakly singular and smooth kernel functions. Meanwhile, the sparse matrix of systems can be correspondingly obtained. The bi-conjugate gradient iterative method is used to solve th
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Ranjit, R. Dhunde. "Double Laplace Transform Method for Solving Fractional Fourth-Order Partial Integro-Differential Equations with Weakly Singular Kernel." Indian Journal of Science and Technology 17, no. 36 (2024): 3712–18. https://doi.org/10.17485/IJST/v17i36.2005.

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Abstract <strong>Objectives:</strong>&nbsp;To investigates the solutions of fourth order partial integro-differential equations with high-order non-integer derivatives and weakly singular kernels.&nbsp;<strong>Methods:</strong>&nbsp;Weakly singular kernels present challenges in both analytical and numerical treatments due to their intricate behaviour near singular points. In this article, we introduce a novel approach utilizing the double Laplace transform method to effectively address these challenges.&nbsp;<strong>Findings:</strong>&nbsp;By solving a series of precise and understandable exam
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Aliev, N., and S. Mohammad Hosseini. "A Regularization of Fredholm type singular integral equations." International Journal of Mathematics and Mathematical Sciences 26, no. 2 (2001): 123–28. http://dx.doi.org/10.1155/s0161171201010286.

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We present a method to regularize first and second kind integral equations of Fredholm type with singular kernel. By appropriate application of the Poincaré-Bertrand formula we change such integral equations into a second kind Fredholm's integral equation with at most weakly singular kernel.
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Dissertations / Theses on the topic "Weakly singular kernel"

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Kaboul, Hanane. "Méthodes d'intégration produit pour les équations de Fredholm de deuxième espèce : cas linéaire et non linéaire." Thesis, Lyon, 2016. http://www.theses.fr/2016LYSES024.

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La méthode d'intégration produit a été proposée pour résoudre des équations linéaires de Fredholm de deuxième espèce singulières dont la solution exacte est régulière, au moins continue. Dans ce travail on adapte cette méthode à des équations dont la solution est juste intégrable. On étudie également son extension au cas non linéaire posé dans l'espace des fonctions intégrables. Ensuite, on propose une autre manière de mettre en oeuvre la méthode d'intégration produit : on commence par linéariser l'équation par une méthode de type Newton puis on discrétise les itérations de Newton par la métho
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Chen, Huyuan. "Fully linear elliptic equations and semilinear fractionnal elliptic equations." Thesis, Tours, 2014. http://www.theses.fr/2014TOUR4001/document.

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Cette thèse est divisée en six parties. La première partie est consacrée à l'étude de propriétés de Hadamard et à l'obtention de théorèmes de Liouville pour des solutions de viscosité d'équations aux dérivées partielles elliptiques complètement non-linéaires avec des termes de gradient,<br>This thesis is divided into six parts. The first part is devoted to prove Hadamard properties and Liouville type theorems for viscosity solutions of fully nonlinear elliptic partial differential equations with gradient term
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Erickson, Andrew Jay. "Simulation of the growth of multiple interacting 2D hydraulic fractures driven by an inviscid fluid." 2012. http://hdl.handle.net/2152/19986.

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In this paper we develop a computational procedure to investigate linear fracture of two-dimensional problems in isotropic linearly elastic media. A symmetric Galerkin boundary element method (SGBEM), based on a weakly singular, weak-form traction integral equation, is adopted to model these fractures. In particular we consider multiple interacting cracks in an unbounded domain subject to internal pressure and remote stress. The growth of the cracks is driven by either linearly dependent injection pressures or volumes in each crack. A variety of crack geometries are investigated.<br>text
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Book chapters on the topic "Weakly singular kernel"

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Laurita, Concetta, and Giuseppe Mastroianni. "Revisiting a quadrature method for CSIE with a weakly singular perturbation kernel." In Problems and Methods in Mathematical Physics. Birkhäuser Basel, 2001. http://dx.doi.org/10.1007/978-3-0348-8276-7_17.

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Panigrahi, Bijaya Laxmi. "Discrete Legendre Collocation Methods for Fredholm–Hammerstein Integral Equations with Weakly Singular Kernel." In Mathematics and Computing. Springer Singapore, 2018. http://dx.doi.org/10.1007/978-981-13-2095-8_25.

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Byun, Sung-Soo, and Peter J. Forrester. "Statistical Properties of GinSE and Elliptic GinSE." In KIAS Springer Series in Mathematics. Springer Nature Singapore, 2024. http://dx.doi.org/10.1007/978-981-97-5173-0_10.

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AbstractEigenvalues of GinSE matrices occur in complex conjugate pairs as for complex GinOE eigenvalues, but now with zero probability of an eigenvalue being real. Also in common with complex GinOE eigenvalues is that the GinSE eigenvalues form a Pfaffian point process, and that their PDF admits a Coulomb gas interpretation with image terms. While the determination of the required skew-orthogonal polynomials is straightforward, the particular form gives a new challenge in relation to analysing the various scaling limits. This is overcome by making use of a certain inhomogeneous partial differe
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Ito, Kazufumi, and Franz Kappel. "On Integro-Differential Equations with Weakly Singular Kernels." In Differential Equations with Applications in Biology, Physics, and Enqineering. CRC Press, 2017. http://dx.doi.org/10.1201/9781315141244-15.

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Ahues, Mario, and Olivier Titaud. "Spectral Approximation of Weakly Singular Integrable Kernels Using Projections." In Integral Methods in Science and Engineering. Birkhäuser Boston, 2002. http://dx.doi.org/10.1007/978-1-4612-0111-3_4.

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Wheeden, Richard L. "Weighted Norm Estimates for Singular Integrals with LlogL Kernels: Regularity of Weak Solutions of Some Degenerate Quasilinear Equations." In Springer Proceedings in Mathematics & Statistics. Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-10545-1_16.

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"VIDEs with weakly singular kernels." In Collocation Methods for Volterra Integral and Related Functional Differential Equations. Cambridge University Press, 2004. http://dx.doi.org/10.1017/cbo9780511543234.008.

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"Cases with Weakly Singular Kernels." In Series on Applied Mathematics. WORLD SCIENTIFIC, 1998. http://dx.doi.org/10.1142/9789812798138_0007.

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"Volterra integral equations with weakly singular kernels." In Collocation Methods for Volterra Integral and Related Functional Differential Equations. Cambridge University Press, 2004. http://dx.doi.org/10.1017/cbo9780511543234.007.

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Panja, M. M., and B. N. Mandal. "Multiscale Solution of Integral Equations with Weakly Singular Kernels." In Wavelet Based Approximation Schemes for Singular Integral Equations. CRC Press, 2020. http://dx.doi.org/10.1201/9780429244070-4.

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Conference papers on the topic "Weakly singular kernel"

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Rungamornrat, Jaroon, Mary F. Wheeler, and Xiuli Gai. "Weakly-Singular Integral Equations for Steady State Flow in Anisotropic Porous Media Containing Discontinuity Surfaces." In ASME 2005 International Mechanical Engineering Congress and Exposition. ASMEDC, 2005. http://dx.doi.org/10.1115/imece2005-80299.

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In this paper, we present the development of the weakly-singular, weak-form fluid pressure and fluid flux integral equations for steady state Darcy’s flow in porous media. The integral equation for fluid flux is required for the treatment of flow in a domain which contains surfaces of discontinuities (e.g. cracks and impermeable surfaces), since the pressure integral equation contains insufficient information about the fluid flux on the surface of discontinuity. In this work, a systematic technique has been established to regularize the conventional fluid pressure and fluid flux integral equat
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Martinez, M. J. "Slug Flow Model for Infiltration Into Fractured Porous Media." In ASME 1999 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 1999. http://dx.doi.org/10.1115/imece1999-1022.

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Abstract A model for transient infiltration into a periodically fractured porous layer is presented. The fracture is treated as a permeable-walled slot and the moisture distribution is in the form of a slug behind an advancing meniscus. The wicking of moisture from the fracture to the unsaturated porous matrix is a nonlinear diffusion process and is approximated by self-similar solutions. The resulting model is a nonlinear Volterra integral equation with a weakly singular kernel. Numerical analysis provides solutions over a wide range of the parameter space and reveals the asymptotic forms of
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Pedas, Arvet, Enn Tamme, and Mikk Vikerpuur. "Numerical solution of fractional integro-differential equations with weakly singular kernels." In CENTRAL EUROPEAN SYMPOSIUM ON THERMOPHYSICS 2019 (CEST). AIP Publishing, 2019. http://dx.doi.org/10.1063/1.5114133.

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Chiang, Shihchung. "Bounded Issues on a Class of Integral Equations with Weakly Singular Kernels." In 2022 International Conference on Engineering and Emerging Technologies (ICEET). IEEE, 2022. http://dx.doi.org/10.1109/iceet56468.2022.10007179.

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Pedas, Arvet, and Mikk Vikerpuur. "High order methods for multi-term fractional integro-differential equations with weakly singular kernels." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2020. AIP Publishing, 2022. http://dx.doi.org/10.1063/5.0081325.

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Wang, Yifei, Jin Huang, and Hu Li. "Bernoulli polynomial approximation method for solving the multi-dimensional Volterra integral equations with variable-order weakly singular kernels." In 2023 3rd International Conference on Applied Mathematics, Modelling and Intelligent Computing (CAMMIC 2023), edited by Xuebin Chen and Hari Mohan Srivastava. SPIE, 2023. http://dx.doi.org/10.1117/12.2685919.

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Reports on the topic "Weakly singular kernel"

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Makroglou, A., and E. J. Kansa. Multiquadric collocation methods in the numerical solution of Volterra integral equations with weakly singular kernels. Office of Scientific and Technical Information (OSTI), 1993. http://dx.doi.org/10.2172/10156921.

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