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High order compact solution of the one‐space‐dimensional linear hyperbolic equation
Author(s) -
Mohebbi Akbar,
Dehghan Mehdi
Publication year - 2008
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20313
Subject(s) - mathematics , hyperbolic partial differential equation , discretization , collocation (remote sensing) , mathematical analysis , partial differential equation , orthogonal collocation , ftcs scheme , collocation method , finite difference method , differential equation , ordinary differential equation , differential algebraic equation , remote sensing , geology
In this article, we introduce a high‐order accurate method for solving one‐space dimensional linear hyperbolic equation. We apply a compact finite difference approximation of fourth order for discretizing spatial derivative of linear hyperbolic equation and collocation method for the time component. The main property of this method additional to its high‐order accuracy due to the fourth order discretization of spatial derivative, is its unconditionally stability. In this technique the solution is approximated by a polynomial at each grid point that its coefficients are determined by solving a linear system of equations. Numerical results show that the compact finite difference approximation of fourth order and collocation method produce a very efficient method for solving the one‐space‐dimensional linear hyperbolic equation. We compare the numerical results of this paper with numerical results of (Mohanty, Appl Math Lett 17 (2004), 101–105).© 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2008