159
Views
26
CrossRef citations to date
0
Altmetric
Section B

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

Pages 3030-3038 | Received 29 Aug 2008, Accepted 09 Mar 2009, Published online: 30 Jun 2010

References

  • Gourley, A. R. , and Mitchell, A. R. , 1969. A classification of split difference methods for hyperbolic equations in several space dimensions , SIAM J. Numer. Anal. 6 (1969), pp. 62–71.
  • Hairer, E. , Norsett, S. P. , and Wanner, G. , 1993. Solving Ordinary Differential Equations I . Springer-Verlag; 1993.
  • Jain, M. K. , 1987. Numerical Solution of Differential Equations . New Delhi: Wiley Eastern Ltd; 1987.
  • Karaa, S. , 2006. A high-order compact ADI method for solving three-dimensional unsteady convection-diffusion problems , Numer. Methods Partial Differential Equations 22 (2006), pp. 983–993.
  • Karaa, S. , and Zhang, J. , 2004. High order ADI method for solving unsteady convection-diffusion problems , J. Comput. Phys. 198 (2004), pp. 1–9.
  • Lees, M. , 1962. Alternating direction implicit methods for hyperbolic differential equations , J. Soc. Indust. Appl. Math. 10 (1962), pp. 610–616.
  • Mohanty, R. K. , 2004. An operator splitting method for an unconditionally stable difference scheme for a linear hyperbolic equation with variable coefficients in two space dimensions , Appl. Math. Comput. 152 (2004), pp. 799–806.
  • Mohanty, R. K. , 2005. An operator splitting technique for an unconditionally stable difference method for a linear three space dimensional hyperbolic equation with variable coefficients , Appl. Math. Comput. 162 (2005), pp. 549–557.
  • Mohanty, R. K. , 2009. New unconditionally stable difference schemes for the solution of multi-domensional telegraphic equations , Int. J. Comput. Math. 36 (2009), pp. 2061–2071.
  • Mohanty, R. K. , and Jain, M. K. , 2001. An unconditionally stable alternating direction implicit scheme for the two space dimensional linear hyperbolic equation , Numer. Methods Partial Differential Equations 22 (2001), pp. 983–993.
  • Mohanty, R. K. , Jain, M. K. , and George, K. , 1996. High order difference schemes for the system of two space dimensional second order non-linear hyperbolic equation with variable coefficients , J. Comput. Appl. Math. 70 (1996), pp. 231–243.
  • Mohanty, R. K. , Jain, M. K. , and Arora, U. , 2002. An unconditionally stable ADI method for the linear hyperbolic equation in three space dimensions , Int. J. Comput. Math. 79 (2002), pp. 133–142.

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:

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:

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.