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High order finite difference schemes with application to wave propagation problems

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High order finite difference schemes with application to wave propagation problems RENDICONTI del SEMINARIO MATEMATICO della UNIVERSITÀ DI PADOVA MARIAANTONIETTA PIROZZI High order finite difference schemes with application to wave propagation problems Rendiconti del Seminario Matematico della Università di Padova, tome 106 (2001), p. 83-110. <http://www.numdam.org/item?id=RSMUP_2001__106__83_0> © Rendiconti del Seminario Matematico della Università di Padova, 2001, tous droits réservés. L’accès aux archives de la revue « Rendiconti del Seminario Matematico della Università di Padova » (http://rendiconti.math.unipd.it/) implique l’ac- cord avec les conditions générales d’utilisation (http://www.numdam.org/legal. php). Toute utilisation commerciale ou impression systématique est consti- tutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/ High Order Finite Difference Schemes with Application to Wave Propagation Problems. MARIA ANTONIETTA PIROZZI (*) ABSTRACT - We consider the approximate solution to wave propagation problems by a family of fully discrete finite difference implicit schemes already proposed in [1]. The stability of mixed initial boundary-value problems is investigated, since this is an essential aspect of the practical application of a numerical method into a working code. The required boundary data are recovered through space-time extrapolation formulas and their effect on the overall accuracy is also esti- mated. A wide series of computational experiments is performed to illustrate the behaviour of the schemes for scalar and vector equations. The features of the boundary treatments are tested and the theoretical error predictions are shown to be in broad agreement with the numerical results. 1. Introduction. The development of numerical schemes remains a very activ

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