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International Journal of Computer Mathematics Volume 88, 2011 - Issue 15
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Section B

Quasi-wavelet based numerical method for fourth-order partial integro-differential equations with a weakly singular kernel

Xuehua Yang Department of Mathematics, Hunan Normal University, 410081, Changsha, Hunan, ChinaCorrespondence[email protected]
,
Da Xu Department of Mathematics, Hunan Normal University, 410081, Changsha, Hunan, ChinaCorrespondence[email protected]
&
Haixiang Zhang Department of Mathematics, Hunan Normal University, 410081, Changsha, Hunan, China
Pages 3236-3254 | Received 04 Jul 2010, Accepted 02 May 2011, Published online: 14 Jul 2011

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Shahid S. Siddiqi & Saima Arshed. (2015) Numerical solution of time-fractional fourth-order partial differential equations. International Journal of Computer Mathematics 92:7, pages 1496-1518.
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Haixiang Zhang & Xuli Han. (2013) Quasi-wavelet method for time-dependent fractional partial differential equation. International Journal of Computer Mathematics 90:11, pages 2491-2507.
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Song-Hua Li, Wei Lin & Jun Xian. (2013) A compression technique for the boundary integral equation reduced from Helmholtz equation. International Journal of Computer Mathematics 90:3, pages 577-593.
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Articles from other publishers (24)

Ziyi Zhou, Haixiang Zhang & Xuehua Yang. (2022) The compact difference scheme for the fourth‐order nonlocal evolution equation with a weakly singular kernel. Mathematical Methods in the Applied Sciences 46:5, pages 5422-5447.
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Hadi Mohammadi-Firouzjaei, Hojatollah Adibi & Mehdi Dehghan. (2023) Study of the backward difference and local discontinuous Galerkin (LDG) methods for solving fourth-order partial integro-differential equations (PIDEs) with memory terms: Stability analysis. Applied Numerical Mathematics 184, pages 567-580.
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M Taghipour & H Aminikhah. (2022) A difference scheme based on cubic B-spline quasi-interpolation for the solution of a fourth-order time-fractional partial integro-differential equation with a weakly singular kernel. Sādhanā 47:4.
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Lijiao Wu, Haixiang Zhang, Xuehua Yang & Furong Wang. (2022) A second-order finite difference method for the multi-term fourth-order integral–differential equations on graded meshes. Computational and Applied Mathematics 41:7.
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Farhad Fakhar‐Izadi. (2020) Fully spectral‐Galerkin method for the one‐ and two‐dimensional fourth‐order time‐fractional partial integro‐differential equations with a weakly singular kernel. Numerical Methods for Partial Differential Equations 38:2, pages 160-176.
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A. T. Assanova & S. N. Nurmukanbet. (2022) A Solvability of a Problem for a Fredholm Integro-Differential Equation with Weakly Singular Kernel. Lobachevskii Journal of Mathematics 43:1, pages 182-191.
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Xingguo Liu, Xuehua Yang, Haixiang Zhang & Yanling Liu. (2021) Discrete singular convolution for fourth-order multi-term time fractional equation. Tbilisi Mathematical Journal 14:2.
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A. T. Assanova. (2021) A Two-Point Boundary Value Problem for a Fourth Order Partial Integro-Differential Equation. Lobachevskii Journal of Mathematics 42:3, pages 526-535.
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Xinfei Liu & Xiaoyuan Yang. (2021) Mixed finite element method for the nonlinear time-fractional stochastic fourth-order reaction–diffusion equation. Computers & Mathematics with Applications 84, pages 39-55.
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Wenlin Qiu, Da Xu & Jing Guo. (2021) The Crank-Nicolson-type Sinc-Galerkin method for the fourth-order partial integro-differential equation with a weakly singular kernel. Applied Numerical Mathematics 159, pages 239-258.
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SACHIN KUMAR, PRASHANT PANDEY, J. F. GÓMEZ-AGUILAR & D. BALEANU. (2020) DOUBLE-QUASI-WAVELET NUMERICAL METHOD FOR THE VARIABLE-ORDER TIME FRACTIONAL AND RIESZ SPACE FRACTIONAL REACTION–DIFFUSION EQUATION INVOLVING DERIVATIVES IN CAPUTO–FABRIZIO SENSE. Fractals 28:08, pages 2040047.
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Sachin Kumar, Jinde Cao & Xiaodi Li. (2020) A Numerical Method for Time-Fractional Reaction-Diffusion and Integro Reaction-Diffusion Equation Based on Quasi-Wavelet. Complexity 2020, pages 1-11.
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Sachin Kumar & Dumitru Baleanu. (2020) A New Numerical Method for Time Fractional Non-linear Sharma-Tasso-Oliver Equation and Klein-Gordon Equation With Exponential Kernel Law. Frontiers in Physics 8.
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Da Xu, Wenlin Qiu & Jing Guo. (2019) 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 36:2, pages 439-458.
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Sachin Kumar & Prashant Pandey. (2020) Quasi wavelet numerical approach of non-linear reaction diffusion and integro reaction-diffusion equation with Atangana–Baleanu time fractional derivative. Chaos, Solitons & Fractals 130, pages 109456.
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Xiaoyong Xu & Da Xu. (2018) 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 37:4, pages 4145-4168.
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A. Babaaghaie & K. Maleknejad. (2017) Numerical solution of integro-differential equations of high order by wavelet basis, its algorithm and convergence analysis. Journal of Computational and Applied Mathematics 325, pages 125-133.
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Saima Arshed. (2017) B-spline solution of fractional integro partial differential equation with a weakly singular kernel. Numerical Methods for Partial Differential Equations 33:5, pages 1565-1581.
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Saima Arshed. (2016) Quintic B-spline method for time-fractional superdiffusion fourth-order differential equation. Mathematical Sciences 11:1, pages 17-26.
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Hira Tariq & Ghazala Akram. (2017) Quintic spline technique for time fractional fourth-order partial differential equation. Numerical Methods for Partial Differential Equations 33:2, pages 445-466.
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Man Luo, Da Xu, Limei Li & Xuehua Yang. (2014) Quasi Wavelet based numerical method for Volterra integro-differential equations on unbounded spatial domains. Applied Mathematics and Computation 227, pages 509-517.
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Man Luo, Da Xu & Limei Li. (2015) Crank-Nicolson Quasi-Wavelet Based Numerical Method for Volterra Integro-Differential Equations on Unbounded Spatial Domains. East Asian Journal on Applied Mathematics 3:4, pages 283-292.
Crossref
Xuehua Yang, Da Xu & Haixiang Zhang. (2013) Crank–Nicolson/quasi-wavelets method for solving fourth order partial integro-differential equation with a weakly singular kernel. Journal of Computational Physics 234, pages 317-329.
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Haixiang Zhang, Xuli Han & Xuehua Yang. (2013) Quintic B-spline collocation method for fourth order partial integro-differential equations with a weakly singular kernel. Applied Mathematics and Computation 219:12, pages 6565-6575.
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