New unconditionally stable difference schemes for the solution of multi-dimensional telegraphic equations

Abstract

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.

Keywords:

• linear hyperbolic equation
• telegraphic equation
• damped wave equation
• ADI method
• unconditionally stable
• RMS errors

2000 AMS Subject Classification :

• 65M06
• 65M12

CCS Category :

• G1.8

Acknowledgements

The author thanks the reviewers for their valuable suggestions, which greatly improved the standard of the paper.