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Zbl 1151.65071
Mohebbi, Akbar; Dehghan, Mehdi
High order compact solution of the one-space-dimensional linear hyperbolic equation. (English)
[J] Numer. Methods Partial Differ. Equations 24, No. 5, 1222-1235 (2008). ISSN 0749-159X; ISSN 1098-2426/e

Summary: 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 {\it R. K. Mohanty} [Appl. Math. Lett. 17, No. 1, 101--105 (2004; Zbl 1046.65076)].

MSC 2000:: *65M06 Finite difference methods (IVP of PDE)
65M70 Spectral, collocation and related methods (IVP of PDE)
35L15 Second order hyperbolic equations, initial value problems

Keywords: collocation; compact finite difference scheme; linear hyperbolic equation; telegraph equation; high accuracy

Citations: Zbl 1046.65076

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