Abstract

PINEROS-CANAS, Juan Carlos  and  GARZON-ALVARADO, Diego Alexander. About a Numeric Solution of the Wave Equation. Ing. Univ. [online]. 2009, vol.13, n.2, pp.387-409. ISSN 0123-2126.

The numerical solution of partial differential equations that evolve over time is a research field in constant development. In this paper on the computational solution to the wave equation, two algorithms of time integration are used: the Newmark method and the finite difference method (FDM). The Newmark method has a high precision and excellent convergence rate compared to the FDM. The FDM can be easily implemented. In an effort to compare these two methods, two typical problems using FORTRAN were implemented: first, a square membrane completely fixed at its edges with an initial velocity in the center, and second, a simply supported beam with an initial velocity at one of its ends. These test problems are discretized in the space domain through the finite element method, and in the time domain through the Newmark method and the FDM. The results show that the Newmark method allows using time steps that are greater than those of the FDM, but present a higher numerical oscillation. These results are expected to be the source of initial data for a subsequent comparison with other methods.

Keywords : Wave equations; differential equations; telecommunication.

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