Solving 2D-wave problems by the iterative differential quadrature method

Abstract

In this paper, the numerical stability of an iterative method based on differential quadrature (DQ) rules when applied to solve a two-dimensional (2D) wave problem is discussed. The physical model of a vibrating membrane, with different initial conditions, is considered. The stability analysis is performed by the matrix method generalized for a 2D space-time domain. This method was presented few years ago by the same author as an analytical support to check the stability of the iterative differential quadrature method in 1D space-time domains. The stability analysis confirms here the conditionally stable nature of the method. The accuracy of the solution is discussed too.

Keywords:

• discretized systems
• quadrature rules
• numerical stability
• accuracy

2010 AMS Subject Classifications :

• 65M12
• 65M22
• 65Z99
• 35L20
• 37M05

Acknowledgements

This work was partially funded by INPES S.p.A. The author is indebted to team at INPES for executing numerical simulations.