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International Journal of Computer Mathematics Volume 97, 2020 - Issue 10
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Original Articles

A formally second-order BDF finite difference scheme for the integro-differential equations with the multi-term kernels

Wenlin Qiua Key Laboratory of Computing and Stochastic Mathematics (Ministry of Education), School of Mathematics and Statistics, Hunan Normal University, Changsha, People's Republic of ChinaCorrespondence[email protected] [email protected]
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Da Xua Key Laboratory of Computing and Stochastic Mathematics (Ministry of Education), School of Mathematics and Statistics, Hunan Normal University, Changsha, People's Republic of ChinaView further author information
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Hongbin Chenb Institute of Mathematics and Physics, College of Science, Central South University of Forestry and Technology, Changsha, People's Republic of China;c Changsha University of Science and Technology, Changsha, People's Republic of ChinaORCID Iconhttps://orcid.org/0000-0002-8989-3743View further author information
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Pages 2055-2073 | Received 29 Nov 2018, Accepted 30 Sep 2019, Published online: 15 Oct 2019

Citations (21)

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Biao Yang, Haixiang Zhang, Xiaoxuan Jiang & Xuehua Yang. (2023) An implicit difference scheme for the fourth-order nonlinear partial integro-differential equations. Applicable Analysis 102:8, pages 2314-2337.
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Articles from other publishers (20)

Qingqing Tian, Xuehua Yang, Haixiang Zhang & Da Xu. (2023) An implicit robust numerical scheme with graded meshes for the modified Burgers model with nonlocal dynamic properties. Computational and Applied Mathematics 42:6.
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Tao Guo, Omid Nikan, Wenlin Qiu & Da Xu. (2023) Localized meshless approaches based on theta method and BDF2 for nonlinear Sobolev equation arising from fluid dynamics. Communications in Nonlinear Science and Numerical Simulation 117, pages 106989.
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Y. Cao, O. Nikan & Z. Avazzadeh. (2023) A localized meshless technique for solving 2D nonlinear integro-differential equation with multi-term kernels. Applied Numerical Mathematics 183, pages 140-156.
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Menglian Li, Omid Nikan, Wenlin Qiu & Da Xu. (2022) An efficient localized meshless collocation method for the two-dimensional Burgers-type equation arising in fluid turbulent flows. Engineering Analysis with Boundary Elements 144, pages 44-54.
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Leijie Qiao, Jing Guo & Wenlin Qiu. (2022) Fast BDF2 ADI methods for the multi-dimensional tempered fractional integrodifferential equation of parabolic type. Computers & Mathematics with Applications 123, pages 89-104.
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Qingqing Tian, Haixiang Zhang, Xuehua Yang & Xiaoxuan Jiang. (2022) An implicit difference scheme for the fourth-order nonlinear non-local PIDEs with a weakly singular kernel. Computational and Applied Mathematics 41:7.
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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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Xiaoxuan Jiang, Xuehua Yang, Haixiang Zhang & Qingqing Tian. (2022) An Implicit Difference Scheme for the Fourth-Order Nonlinear Evolution Equation with Multi-Term Riemann–Liouvile Fractional Integral Kernels. Fractal and Fractional 6:8, pages 443.
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Wenlin Qiu, Da Xu & Jing Guo. (2020) A formally second‐order backward differentiation formula Sinc‐collocation method for the Volterra integro‐differential equation with a weakly singular kernel based on the double exponential transformation . Numerical Methods for Partial Differential Equations 38:4, pages 830-847.
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Leijie Qiao, Da Xu, Bo Tang & Jun Zhou. (2022) Fast ADI difference/compact difference schemes for the nonlocal evolution equation with weakly singular kernels in three dimensions. Mathematics and Computers in Simulation 194, pages 329-347.
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Huifa Jiang & Da Xu. (2021) An efficient Sinc‐collocation method by the single exponential transformation for the nonlinear fourth‐order partial integro‐differential equation with multiterm kernels. Mathematical Methods in the Applied Sciences 45:5, pages 3166-3182.
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Xuehua Yang, Wenlin Qiu, Haifan Chen & Haixiang Zhang. (2022) Second-order BDF ADI Galerkin finite element method for the evolutionary equation with a nonlocal term in three-dimensional space. Applied Numerical Mathematics 172, pages 497-513.
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Zhengang Zhao, Yunying Zheng & Xianglin Zeng. (2022) Finite element approximation of fractional hyperbolic integro-differential equation. AIMS Mathematics 7:8, pages 15348-15369.
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. (2022) The efficient ADI Galerkin finite element methods for the three-dimensional nonlocal evolution problem arising in viscoelastic mechanics. Discrete and Continuous Dynamical Systems - B 0:0, pages 0-0.
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Leijie Qiao, Wenlin Qiu & Da Xu. (2021) A second-order ADI difference scheme based on non-uniform meshes for the three-dimensional nonlocal evolution problem. Computers & Mathematics with Applications 102, pages 137-145.
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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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Shantiram Mahata & Rajen Kumar Sinha. (2021) Finite Element Method for Fractional Parabolic Integro-Differential Equations with Smooth and Nonsmooth Initial Data. Journal of Scientific Computing 87:1.
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Wenlin Qiu, Da Xu & Jing Guo. (2021) Numerical solution of the fourth-order partial integro-differential equation with multi-term kernels by the Sinc-collocation method based on the double exponential transformation. Applied Mathematics and Computation 392, pages 125693.
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Yanling Liu, Xuehua Yang, Haixiang Zhang & Yuan Liu. (2021) Analysis of BDF2 finite difference method for fourth-order integro-differential equation. Computational and Applied Mathematics 40:2.
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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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