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Ain Shams Engineering Journal, 2022 We presented an interpolation method for solving weakly singular Volterra integral equations of the second kind (SVK2). The method based on the barycentric Lagrange interpolation.. For the chosen nodes of the two singular kernel variables, we created two
E.S. Shoukralla +3 more
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Fractal and Fractional, 2021 We propose a fractional-order shifted Jacobi–Gauss collocation method for variable-order fractional integro-differential equations with weakly singular kernel (VO-FIDE-WSK) subject to initial conditions.
Mohamed A. Abdelkawy +4 more
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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
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Journal of Mathematics, 2021 In this paper, we present a numerical scheme for finding numerical solution of a class of weakly singular nonlinear fractional integro-differential equations. This method exploits the alternative Legendre polynomials.
Guodong Shi, Yanlei Gong, Mingxu Yi
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Reproducing kernel method for a class of weakly singular Fredholm integral equations
Journal of Taibah University for Science, 2018 Numerical methods for solving integral equations have been the focus of much research, including reproducing kernel methods. We present a new algorithm to solve weakly singular Fredholm integral equations (WSFIEs). The advantage of this method is that it
Azizallah Alvandi, Mahmoud Paripour
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Computers and Mathematics With Applications, 2020 We present an alternating direction implicit (ADI) difference scheme for the multi-term time-fractional integro-differential equation with a weakly singular kernel. The Caputo fractional derivative is discretized by L1 method and the integro-differential
, Da Xu
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Journal of Computational and Applied Mathematics, 2019 In this paper, we consider Legendre multi-Galerkin methods to solve Fredholm integral equations of the second kind with weakly singular kernel and the corresponding eigenvalue problem.
Bijaya Laxmi Panigrahi +2 more
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Journal of Computational and Applied Mathematics, 2019 A second-order accurate numerical method with graded meshes is proposed and analyzed for an evolution equation with a weakly singular kernel. The graded meshes are employed to compensate for the singular behavior of the exact solution at t = 0 .
, Da Xu, Hongbin Chen
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Fractal and Fractional, 2021 Fractional differential equations can present the physical pathways with the storage and inherited properties due to the memory factor of fractional order.
Tayyaba Akram +4 more
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