Advanced search
Publication Cover
International Journal of Computer Mathematics Volume 87, 2010 - Issue 13
Submit an article Journal homepage
159
Views
26
CrossRef citations to date
0
Altmetric
Section B

Unconditionally stable ADI scheme of higher-order for linear hyperbolic equations

Samir Karaa Department of Mathematics and Statistics, Sultan Qaboos University , P.O. Box 36, Al-Khod 123, Muscat, Sultanate of Oman
Pages 3030-3038 | Received 29 Aug 2008, Accepted 09 Mar 2009, Published online: 30 Jun 2010

Citations (26)

Keep up to date with the latest research on this topic with citation updates for this article.

Subscribe to citation updates

Read on this site (6)

Yunzhi Jiang & Yongbin Ge. (2023) An explicit high-order compact finite difference scheme for the three-dimensional acoustic wave equation with variable speed of sound. International Journal of Computer Mathematics 100:2, pages 321-341.
Read now
Buyun Chen, Dongdong He & Kejia Pan. (2019) A CCD-ADI method for two-dimensional linear and nonlinear hyperbolic telegraph equations with variable coefficients. International Journal of Computer Mathematics 96:5, pages 992-1004.
Read now
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.
Read now
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.
Read now
Hong-Lin Liao & Zhi-Zhong Sun. (2013) A two-level compact ADI method for solving second-order wave equations. International Journal of Computer Mathematics 90:7, pages 1471-1488.
Read now
Dingwen Deng & Chengjian Zhang. (2013) Application of a fourth-order compact ADI method to solve a two-dimensional linear hyperbolic equation. International Journal of Computer Mathematics 90:2, pages 273-291.
Read now

Articles from other publishers (20)

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.
Crossref
Mehmet Emir Köksal. (2023) Recent Developments of Numerical Methods for Analyzing Telegraph Equations. Archives of Computational Methods in Engineering 30:6, pages 3509-3527.
Crossref
R.K. Mohanty & Bishnu Pada Ghosh. (2023) High resolution numerical algorithm of order (2, 4, 4) for 2D quasi-linear hyperbolic equations based on half-step discretization on an unequal grid. Partial Differential Equations in Applied Mathematics 7, pages 100528.
Crossref
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.
Crossref
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.
Crossref
R.K. Mohanty, Bishnu Pada Ghosh & Urvashi Arora. (2022) High precision implicit method for 3D quasilinear hyperbolic equations on a dissimilar domain: Application to 3D telegraphic equation. Computers & Mathematics with Applications 122, pages 93-116.
Crossref
Dingwen Deng & Qiang Wu. (2021) The error estimations of a two-level linearized compact ADI method for solving the nonlinear coupled wave equations. Numerical Algorithms 89:4, pages 1663-1693.
Crossref
R.K. Mohanty & Bishnu Pada Ghosh. (2022) High resolution operator compact implicit half-step approximation for 3D quasi-linear hyperbolic equations and ADI method for 3D telegraphic equation on an irrational domain. Applied Numerical Mathematics 172, pages 446-474.
Crossref
Alexander Zlotnik & Raimondas Čiegis. (2022) On higher-order compact ADI schemes for the variable coefficient wave equation. Applied Mathematics and Computation 412, pages 126565.
Crossref
Yunzhi Jiang & Yongbin Ge. (2020) An explicit fourth-order compact difference scheme for solving the 2D wave equation. Advances in Difference Equations 2020:1.
Crossref
Ajmal Ali & Norhashidah Hj. Mohd. Ali. (2019) On skewed grid point iterative method for solving 2D hyperbolic telegraph fractional differential equation. Advances in Difference Equations 2019:1.
Crossref
R. K. Mohanty & Gunjan Khurana. (2018) A New Fast Algorithm Based on Half-Step Discretization for 3D Quasilinear Hyperbolic Partial Differential Equations. International Journal of Computational Methods 16:01, pages 1850090.
Crossref
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.
Crossref
R. K. Mohanty & Gunjan Khurana. (2017) A New Fast Numerical Method Based on Off-Step Discretization for Two-Dimensional Quasilinear Hyperbolic Partial Differential Equations. International Journal of Computational Methods 14:03, pages 1750031.
Crossref
Dongdong He. (2015) An unconditionally stable spatial sixth-order CCD-ADI method for the two-dimensional linear telegraph equation. Numerical Algorithms 72:4, pages 1103-1117.
Crossref
R.K. Mohanty, Suruchi Singh & Swarn Singh. (2014) A new high order space derivative discretization for 3D quasi-linear hyperbolic partial differential equations. Applied Mathematics and Computation 232, pages 529-541.
Crossref
Dingwen Deng & Chengjian Zhang. (2012) Analysis of a fourth-order compact ADI method for a linear hyperbolic equation with three spatial variables. Numerical Algorithms 63:1, pages 1-26.
Crossref
R.K. Mohanty & Venu Gopal. (2013) A new off-step high order approximation for the solution of three-space dimensional nonlinear wave equations. Applied Mathematical Modelling 37:5, pages 2802-2815.
Crossref
R. K. MOHANTY & VENU GOPAL. (2012) HIGH ACCURACY ARITHMETIC AVERAGE TYPE DISCRETIZATION FOR THE SOLUTION OF TWO-SPACE DIMENSIONAL NONLINEAR WAVE EQUATIONS. International Journal of Modeling, Simulation, and Scientific Computing 03:02, pages 1150005.
Crossref
R. K. Mohanty & Suruchi Singh. (2011) A New High-Order Approximation for the Solution of Two-Space-Dimensional Quasilinear Hyperbolic Equations. Advances in Mathematical Physics 2011, pages 1-22.
Crossref

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.