New unconditionally stable difference schemes for the solution of multi-dimensional telegraphic equations. (English) Zbl 1181.65112

Mohanty, R. K.

Int. J. Comput. Math. 86, No. 12, 2061-2071 (2009).

Summary: New unconditionally stable implicit difference schemes for the numerical solution of multi-dimensional telegraphic equations subject to appropriate initial and Dirichlet boundary conditions are discussed. Alternating direction implicit methods are used to solve two and three space dimensional problems. The resulting system of algebraic equations is solved using a tri-diagonal solver. Numerical results are presented to demonstrate the utility of the proposed methods.

MSC:

65M06	Finite difference methods for initial value and initial-boundary value problems involving PDEs
35L20	Initial-boundary value problems for second-order hyperbolic equations
65M12	Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65F10	Iterative numerical methods for linear systems
65M15	Error bounds for initial value and initial-boundary value problems involving PDEs

Keywords:

linear hyperbolic equation; telegraphic equation; damped wave equation; ADI method; RMS errors; unconditional stability; alternating direction implicit methods; numerical results

References:

[1]	Bohme G., Non-Newtonian Fluid Mechanics (1987)
[2]	Bryksenkova N. K., Combust. Explo. Shock Waves 29 pp 333– (1993)
[3]	DOI: 10.1016/0377-0427(85)90018-4 · Zbl 0579.65073
[4]	DOI: 10.1007/BF01135371
[5]	DOI: 10.1080/0020716031000112312 · Zbl 1043.65101
[6]	DOI: 10.1063/1.369258
[7]	DOI: 10.1103/PhysRevE.62.7918
[8]	DOI: 10.1137/0110046 · Zbl 0111.29204
[9]	DOI: 10.1093/imamat/11.1.105 · Zbl 0259.65085
[10]	DOI: 10.1002/num.20003 · Zbl 1062.65086
[11]	DOI: 10.1002/num.20073 · Zbl 1160.65329
[12]	DOI: 10.1080/00207390210162465 · Zbl 02350371
[13]	DOI: 10.1002/num.6 · Zbl 0982.65096
[14]	DOI: 10.1002/num.1029 · Zbl 0990.65102
[15]	DOI: 10.1016/0020-7225(86)90163-1 · Zbl 0624.76119