##
**An unconditionally stable parallel difference scheme for telegraph equation.**
*(English)*
Zbl 1181.78018

Summary: We use an unconditionally stable parallel difference scheme to solve telegraph equation. This method is based on the domain decomposition concept and uses asymmetric Saul’yev schemes for internal nodes of each sub-domain and the alternating group implicit method for interfacial nodes of the sub-domains. This new method has several advantages, such as: good parallelism, unconditional stability and better accuracy than the original Saul’yev schemes. The details of the implementation and the proof of stability are briefly discussed. Numerical experiments on stability and accuracy are also presented.

### MSC:

78M20 | Finite difference methods applied to problems in optics and electromagnetic theory |

65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |

65Y05 | Parallel numerical computation |

PDF
BibTeX
XML
Cite

\textit{A. Borhanifar} and \textit{R. Abazari}, Math. Probl. Eng. 2009, Article ID 969610, 17 p. (2009; Zbl 1181.78018)

### References:

[1] | J. Gao and G. He, “An unconditionally stable parallel difference scheme for parabolic equations,” Applied Mathematics and Computation, vol. 135, no. 2-3, pp. 391-398, 2003. · Zbl 1037.65083 |

[2] | R. K. Mohanty, M. K. Jain, and U. Arora, “An unconditionally stable ADI method for the linear hyperbolic equation in three space dimensions,” International Journal of Computer Mathematics, vol. 79, no. 1, pp. 133-142, 2002. · Zbl 0995.65093 |

[3] | R. K. Mohanty, “An unconditionally stable difference scheme for the one-space-dimensional linear hyperbolic equation,” Applied Mathematics Letters, vol. 17, no. 1, pp. 101-105, 2004. · Zbl 1046.65076 |

[4] | R. K. Mohanty, “An unconditionally stable finite difference formula for a linear second order one space dimensional hyperbolic equation with variable coefficients,” Applied Mathematics and Computation, vol. 165, no. 1, pp. 229-236, 2005. · Zbl 1070.65076 |

[5] | M. K. Jain, Numerical Solution of Differential Equations, Wiley Eastern, New Delhi, India, 1991. · Zbl 0744.76084 |

[6] | M. S. Sahimi, E. Sundararajan, M. Subramaniam, and N. A. A. Hamid, “The D/Yakonov fully explicit variant of the iterative decomposition method,” Computers & Mathematics with Applications, vol. 42, no. 10-11, pp. 1485-1496, 2001. · Zbl 1013.65085 |

[7] | V. K. Saul/yev, Integration of Equations of Parabolic Type Equation by the Method of Net, Pergamon Press, New York, NY, USA, 1964. · Zbl 0128.11803 |

[8] | D. J. Evans, “Alternating group explicit method for the diffusion equation,” Applied Mathematical Modelling, vol. 9, no. 3, pp. 201-206, 1985. · Zbl 0591.65068 |

[9] | U. M. Ascher, S. J. Ruuth, and B. T. R. Wetton, “Implicit-explicit methods for time dependent partial differential equations,” SIAM Journal on Numerical Analysis, vol. 32, no. 3, pp. 797-823, 1995. · Zbl 0841.65081 |

[10] | R. D. Richtmeyer and K. W. Morton, Difference Method for Initial-Value Problems, Interscince, New York, NY, US, 1967. · Zbl 0155.47502 |

[11] | G. D. Smith, Numerical Solution of Partial Differential Equations: Finite Difference Methods, Oxford University Press, Oxford, UK, 1990. |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.