References
- W.F. Ames: Numerical methods for partial differential equations. Academic Press, 1992.
- J.J. Benito, F. Urena & L. Gravete: Solving parabolic and hyperbolic equations by the generalized finite difference method. J. Comput. Appl. Math. 209 (2007), 208-233. https://doi.org/10.1016/j.cam.2006.10.090
- R.L. Burden & J.D. Faires: Numerical Analysis, Thomson Brooks/Cole, 2005.
- R. Codina: Finite element approximation of the hyperbolic wave equation in mixed form. Comput. Methods Appl. Mech. Engrg. 197 (2008), 1305-1322. https://doi.org/10.1016/j.cma.2007.11.006
- C.N. Dawson & T.F. Dupont: Noniterative domain decomposition for second order hyperbolic problems. Contemp. Math. 157 (1994), 45-52.
-
H. Ding & Y. Zhang: A new unconditionally stable compact difference scheme of O
$({\tau}^2+h^4)$ for the ID linear hyperbolic equation. Appl. Math. Comput. 207 (2009), 236-241. https://doi.org/10.1016/j.amc.2008.10.024 - M.J. Gander & L. Halpern: Absorbing boundary conditions for the wave equation and parallel computing. Math. Comp. 74 (2005), 153-176.
- X. He & T. Lu: A finite element splitting extrapolation for second order hyperbolic equations. SIAM J. Sci. Comput. 31 (2009/10), 4244-4265.
- Y. Jun & T.Z. Mai: ADI method - Domain decomposition. Appl. Numer. Math. 56 (2006), 1092-1107. https://doi.org/10.1016/j.apnum.2005.09.008
- Y. Jun & T.Z. Mai: Rectangular domain decomposition method for parabolic problems. J. Korea Soc. Math. Educ. Ser. B: Pure and Appl. Math. 13 (2006), 281-294.
- Y. Jun: An efficient domain decomposition decomposition method for three-dimensional parabolic problems. Appl. Math. Comput. 215 (2009), 2815-2825. https://doi.org/10.1016/j.amc.2009.09.022
- Y. Jun: A stable noniterative Prediction/Correction domain decomposition method for hyperbolic problems. Appl. Math. Comput. 216 (2010), 2286-2292. https://doi.org/10.1016/j.amc.2010.03.064
-
Y. Liu & H. Li:
$H^{1}$ -Galerkin mixed finite element methods for pseudo-hyperbolic equations. Appl. Math. Comput. 212 (2009), 446-457. https://doi.org/10.1016/j.amc.2009.02.039 - A. Mohebbi & M. Dehghan: High order compact solution of the one-space-dimensional linear hyperbolic equation. Numer. Methods Partial Differential Equations 24 (2008), 1222-1235. https://doi.org/10.1002/num.20313
- R.K. Mohanty: An unconditinally stable finite difference formula for a linear second order one space dimensional hyperbolic equation with variable coefficnents. Appl. Math. Comput. 165 (2005), 229-236. https://doi.org/10.1016/j.amc.2004.07.002
- R.K Mohanty: Stability interval for explicit difference schemes for multi-dimensional second-order hyperbolic equations with significant first-order space derivative terms. Appl. Math. Comput. 190 (2007), 1683-1690. https://doi.org/10.1016/j.amc.2007.02.097
- M. Ramezani, M. Dehghan & M. Razzaghi: Combined finite difference and spectral methods for the numerical solution of hyperbolic equation with an integral condition. Numer. Methods Partial Differential Equations 24 (2008), 1-8. https://doi.org/10.1002/num.20230
- K.K. Sharma & P. Singh: Hyperbolic partial differential-difference equation in the mathematical modeling of neuronal firing and its numerical solution. Appl. Math. Comput. 201 (2008), 229-238. https://doi.org/10.1016/j.amc.2007.12.051
- Z. Zhang & D. Deng: A new alternating-direction finite element method for hyperbolic equation. Numer. Methods Partial Differential Equations 23 (2007), 1530-1559. https://doi.org/10.1002/num.20240