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Smith, G.D. (1985) Numerical Solutions of Partial Differential Equations: Finite Difference Methods. 3rd Edition, Oxford University Press, New York.

has been cited by the following article:

  • TITLE: Comparison of Finite Difference Schemes for the Wave Equation Based on Dispersion

    AUTHORS: Yahya Ali Abdulkadir

    KEYWORDS: Wave Equation, Finite Difference Methods, Dispersion

    JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.3 No.11, November 30, 2015

    ABSTRACT: Finite difference techniques are widely used for the numerical simulation of time-dependent partial differential equations. In order to get better accuracy at low computational cost, researchers have attempted to develop higher order methods by improving other lower order methods. However, these types of methods usually suffer from a high degree of numerical dispersion. In this paper, we review three higher order finite difference methods, higher order compact (HOC), compact Padé based (CPD) and non-compact Padé based (NCPD) schemes for the acoustic wave equation. We present the stability analysis of the three schemes and derive dispersion characteristics for these schemes. The effects of Courant Friedrichs Lewy (CFL) number, propagation angle and number of cells per wavelength on dispersion are studied.