The Crank-Nicolson-type Sinc-Galerkin method for the fourth-order partial integro-differential equation with a weakly singular kernel

Applied Numerical Mathematics ◽

10.1016/j.apnum.2020.09.011 ◽

2021 ◽

Vol 159 ◽

pp. 239-258 ◽

Author(s):

Wenlin Qiu ◽

Da Xu ◽

Jing Guo

Keyword(s):

Differential Equation ◽

Galerkin Method ◽

Fourth Order ◽

Singular Kernel ◽

Weakly Singular Kernel ◽

Integro Differential Equation ◽

Weakly Singular ◽

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Crank–Nicolson/quasi-wavelets method for solving fourth order partial integro-differential equation with a weakly singular kernel

Journal of Computational Physics ◽

10.1016/j.jcp.2012.09.037 ◽

2013 ◽

Vol 234 ◽

pp. 317-329 ◽

Author(s):

Xuehua Yang ◽

Da Xu ◽

Haixiang Zhang

Keyword(s):

Differential Equation ◽

Fourth Order ◽

Singular Kernel ◽

Weakly Singular Kernel ◽

Integro Differential Equation ◽

Weakly Singular ◽

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A semi-discrete scheme for solving fourth-order partial integro-differential equation with a weakly singular kernel using Legendre wavelets method

Computational and Applied Mathematics ◽

10.1007/s40314-017-0566-2 ◽

2018 ◽

Vol 37 (4) ◽

pp. 4145-4168 ◽

Author(s):

Xiaoyong Xu ◽

Da Xu

Keyword(s):

Differential Equation ◽

Fourth Order ◽

Singular Kernel ◽

Legendre Wavelets ◽

Weakly Singular Kernel ◽

Integro Differential Equation ◽

Discrete Scheme ◽

Weakly Singular

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A compact finite difference scheme for the fourth‐order time‐fractional integro‐differential equation with a weakly singular kernel

Numerical Methods for Partial Differential Equations ◽

10.1002/num.22436 ◽

2019 ◽

Vol 36 (2) ◽

pp. 439-458 ◽

Author(s):

Da Xu ◽

Wenlin Qiu ◽

Jing Guo

Keyword(s):

Differential Equation ◽

Finite Difference ◽

Difference Scheme ◽

Fourth Order ◽

Finite Difference Scheme ◽

Singular Kernel ◽

Weakly Singular Kernel ◽

Compact Finite Difference Scheme ◽

Integro Differential Equation ◽

Weakly Singular

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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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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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