Adaptive discretization of an integro-differential equation with a weakly singular convolution kernel

Computer Methods in Applied Mechanics and Engineering ◽

10.1016/j.cma.2003.09.001 ◽

2003 ◽

Vol 192 (51-52) ◽

pp. 5285-5304 ◽

Author(s):

Klas Adolfsson ◽

Mikael Enelund ◽

Stig Larsson

Keyword(s):

Differential Equation ◽

Convolution Kernel ◽

Integro Differential Equation ◽

Weakly Singular ◽

Adaptive Discretization

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Numerical solution of partial integro-differential equation with a weakly singular kernel based on sinc methods

Mathematics and Computers in Simulation ◽

10.1016/j.matcom.2021.05.014 ◽

2021 ◽

Author(s):

Da Xu

Keyword(s):

Differential Equation ◽

Numerical Solution ◽

Singular Kernel ◽

Weakly Singular Kernel ◽

Integro Differential Equation ◽

Sinc Methods ◽

Weakly Singular

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Orthogonal cubic spline basis and its applications to a partial integro-differential equation with a weakly singular kernel

Computational and Applied Mathematics ◽

10.1007/s40314-021-01442-5 ◽

2021 ◽

Vol 40 (2) ◽

Author(s):

J. Alavi ◽

H. Aminikhah

Keyword(s):

Differential Equation ◽

Cubic Spline ◽

Singular Kernel ◽

Weakly Singular Kernel ◽

Integro Differential Equation ◽

Weakly Singular ◽

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Compact finite difference scheme for the solution of a time fractional partial integro-differential equation with a weakly singular kernel

Mathematical Methods in the Applied Sciences ◽

10.1002/mma.4549 ◽

2017 ◽

Vol 40 (18) ◽

pp. 7627-7639 ◽

Author(s):

Akbar Mohebbi

Keyword(s):

Differential Equation ◽

Finite Difference ◽

Difference Scheme ◽

Finite Difference Scheme ◽

Singular Kernel ◽

Weakly Singular Kernel ◽

Compact Finite Difference Scheme ◽

Compact Finite Difference ◽

Integro Differential Equation ◽

Weakly Singular

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An ADI difference scheme based on fractional trapezoidal rule for fractional integro-differential equation with a weakly singular kernel

Applied Mathematics and Computation ◽

10.1016/j.amc.2019.02.022 ◽

2019 ◽

Vol 354 ◽

pp. 103-114 ◽

Author(s):

Leijie Qiao ◽

Da Xu ◽

Zhibo Wang

Keyword(s):

Differential Equation ◽

Difference Scheme ◽

Trapezoidal Rule ◽

Singular Kernel ◽

Weakly Singular Kernel ◽

Integro Differential Equation ◽

Weakly Singular

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Weak Galerkin finite element method for the parabolic integro-differential equation with weakly singular kernel

Computational and Applied Mathematics ◽

10.1007/s40314-019-0807-7 ◽

2019 ◽

Vol 38 (2) ◽

Author(s):

Jun Zhou ◽

Da Xu ◽

Xiuxiu Dai

Keyword(s):

Differential Equation ◽

Finite Element Method ◽

Finite Element ◽

Singular Kernel ◽

Galerkin Finite Element Method ◽

Weak Galerkin ◽

Weakly Singular Kernel ◽

Galerkin Finite Element ◽

Integro Differential Equation ◽

Weakly Singular

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Alternating direction implicit difference scheme for the multi-term time-fractional integro-differential equation with a weakly singular kernel

Computers & Mathematics with Applications ◽

10.1016/j.camwa.2019.06.027 ◽

2020 ◽

Vol 79 (2) ◽

pp. 244-255 ◽

Author(s):

Jun Zhou ◽

Da Xu

Keyword(s):

Differential Equation ◽

Difference Scheme ◽

Singular Kernel ◽

Implicit Difference Scheme ◽

Weakly Singular Kernel ◽

Alternating Direction Implicit ◽

Integro Differential Equation ◽

Weakly Singular ◽

Alternating Direction

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An Inverse Problem for an Integro-Differential Equation with a Convolution Kernel Dependent on the Spectral Parameter

Results in Mathematics ◽

10.1007/s00025-019-1073-0 ◽

2019 ◽

Vol 74 (4) ◽

Author(s):

Natalia P. Bondarenko

Keyword(s):

Differential Equation ◽

Inverse Problem ◽

Spectral Parameter ◽

Convolution Kernel ◽

Integro Differential Equation

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Numerical solution of nonlinear weakly singular partial integro-differential equation via operational matrices

Applied Mathematics and Computation ◽

10.1016/j.amc.2016.11.012 ◽

2017 ◽

Vol 298 ◽

pp. 310-321 ◽

Author(s):

Somveer Singh ◽

Vijay Kumar Patel ◽

Vineet Kumar Singh ◽

Emran Tohidi

Keyword(s):

Differential Equation ◽

Numerical Solution ◽

Operational Matrices ◽

Integro Differential Equation ◽

Weakly Singular

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Space–time spectral method for a weakly singular parabolic partial integro-differential equation on irregular domains

Computers & Mathematics with Applications ◽

10.1016/j.camwa.2014.03.016 ◽

2014 ◽

Vol 67 (10) ◽

pp. 1884-1904 ◽

Author(s):

Farhad Fakhar-Izadi ◽

Mehdi Dehghan

Keyword(s):

Differential Equation ◽

Spectral Method ◽

Irregular Domains ◽

Integro Differential Equation ◽

Weakly Singular ◽

Time Spectral Method

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A stable least residue method in reproducing kernel space for solving a nonlinear fractional integro-differential equation with a weakly singular kernel

Applied Numerical Mathematics ◽

10.1016/j.apnum.2020.06.004 ◽

2020 ◽

Vol 157 ◽

pp. 210-222 ◽

Author(s):

Hong Du ◽

Zhong Chen ◽

Tiejun Yang

Keyword(s):

Differential Equation ◽

Reproducing Kernel ◽

Singular Kernel ◽

Kernel Space ◽

Reproducing Kernel Space ◽

Weakly Singular Kernel ◽

Integro Differential Equation ◽

Weakly Singular

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