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Solving 2D-wave problems by the Iterative Differential Quadrature method
Taylor & Francis
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.
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