High-order methods for the acoustic wave equation in one space dimension

Juliano Deividy B. Santos¹; Abimael Fernando Dourado Loula¹

¹ Laboratório Nacional de Computação Cinentífica

doi:10.20906/CPS/CILAMCE2017-0583

Resumo

Finite difference methodologies are classically generated by Taylor series expansions. In this work we present a methodology to obtain finite difference approximations of different orders for the acoustic wave equation in one space dimension, aiming at obtaining high order methods compared to the classical ones. Unlike the usual methodologies, we will use polynomial basis functions in space and time to obtain coefficients stencils (compact or not). To this end, bases of characteristic polynomials are used to obtain the coefficients. For stencils with seven and nine points and time step of the same order as the spatial step, higher order methods are obtained compared to the classical methodologies. Stability analysis is performed showing that the conditions for the proposed methodology are less restrictive than those corresponding to the classical finite difference discretizations obtained by Taylor series approaches. Numerical experiments are conducted, corroborating the orders of convergence analysis.

Palavras-chave: Finite Differences; Acoustic wave equation; Characteristic polynomials