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International Journal of Computer Mathematics Volume 90, 2013 - Issue 2
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Section B

Application of a fourth-order compact ADI method to solve a two-dimensional linear hyperbolic equation

Dingwen Deng School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, 430074, China; College of Mathematics and Information Science, Nanchang Hangkong University, Nanchang, 330063, China
&
Chengjian Zhang School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, 430074, ChinaCorrespondence[email protected]
Pages 273-291 | Received 06 Mar 2012, Accepted 12 Jul 2012, Published online: 28 Aug 2012

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Dingwen Deng & Yaolin Jiang. (2017) Two-Level Finite Difference Methods for Simulating the High-Dimensional Lagging Models of Heat Conduction. Numerical Functional Analysis and Optimization 38:7, pages 831-860.
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Wendi Qin, Deqiong Ding & Xiaohua Ding. (2015) Unconditionally positivity and boundedness preserving schemes for a FitzHugh–Nagumo equation. International Journal of Computer Mathematics 92:10, pages 2198-2218.
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Dingwen Deng. (2014) Accuracy improvement of a multistep splitting method for nonlinear viscous wave equations. International Journal of Computer Mathematics 91:8, pages 1755-1774.
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Qifeng Zhang, Chengjian Zhang & Dingwen Deng. (2014) Compact alternating direction implicit method to solve two-dimensional nonlinear delay hyperbolic differential equations. International Journal of Computer Mathematics 91:5, pages 964-982.
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Alexander Zlotnik & Timofey Lomonosov. (2024) On stability and error bounds of an explicit in time higher-order vector compact scheme for the multidimensional wave and acoustic wave equations. Applied Numerical Mathematics 195, pages 54-74.
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Qing Li & Huanzhen Chen. (2023) An efficient compact difference-proper orthogonal decomposition algorithm for fractional viscoelastic plate vibration model. Computers & Mathematics with Applications 151, pages 190-214.
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Mehmet Emir Köksal. (2023) Recent Developments of Numerical Methods for Analyzing Telegraph Equations. Archives of Computational Methods in Engineering 30:6, pages 3509-3527.
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Qing Li, Huanzhen Chen & Hong Wang. (2023) A proper orthogonal decomposition-compact difference algorithm for plate vibration models. Numerical Algorithms.
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S. Karthick & V. Subburayan. (2023) Alternative Direction Implicit Method for Solving First Order 2D Hyperbolic Delay Differential Equations. Computational Mathematics and Mathematical Physics 63:5, pages 779-793.
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R. K. Mohanty & Bishnu Pada Ghosh. (2022) A high-resolution bi-parametric unconditionally stable ADI method for 2D uniform transmission line equation. Computational and Applied Mathematics 41:7.
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Alexander Zlotnik & Raimondas Čiegis. (2022) On higher-order compact ADI schemes for the variable coefficient wave equation. Applied Mathematics and Computation 412, pages 126565.
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Paul Castillo & Sergio Gómez. (2021) An interpolatory directional splitting-local discontinuous Galerkin method with application to pattern formation in 2D/3D. Applied Mathematics and Computation 397, pages 125984.
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Jiankang Liu & Suying Zhang. (2020) A New Numerical Approximation Method for Two-Dimensional Wave Equation with Neumann Damped Boundary. Complexity 2020, pages 1-14.
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B. Otero, O. Rojas, F. Moya & J.E. Castillo. (2020) Alternating direction implicit time integrations for finite difference acoustic wave propagation: Parallelization and convergence. Computers & Fluids 205, pages 104584.
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Ji Lin, Fen Chen, Yuhui Zhang & Jun Lu. (2019) An accurate meshless collocation technique for solving two-dimensional hyperbolic telegraph equations in arbitrary domains. Engineering Analysis with Boundary Elements 108, pages 372-384.
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Ben-Dian Nie & Bing-Yang Cao. (2019) Three mathematical representations and an improved ADI method for hyperbolic heat conduction. International Journal of Heat and Mass Transfer 135, pages 974-984.
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Z. Soori & A. Aminataei. (2018) Effect of the nodes near boundary points on the stability analysis of sixth-order compact finite difference ADI scheme for the two-dimensional time fractional diffusion-wave equation. Transactions of A. Razmadze Mathematical Institute 172:3, pages 582-605.
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Dingwen Deng. (2018) Unified compact ADI methods for solving nonlinear viscous and nonviscous wave equations. Chinese Journal of Physics 56:6, pages 2897-2915.
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Geng Zhang, Dan Cai & Yong Du. (2017) Improved ADI Scheme for Linear Hyperbolic Equations: Extension to Nonlinear Cases and Compact ADI Schemes. Journal of Scientific Computing 72:2, pages 500-521.
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