Geodesic
Numerical solution of second order one-dimensional linear hyperbolic equation using trigonometric wavelets
Kybernetika, Tome 48 (2012) no. 5, pp. 939-957 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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A numerical technique is presented for the solution of second order one dimensional linear hyperbolic equation. This method uses the trigonometric wavelets. The method consists of expanding the required approximate solution as the elements of trigonometric wavelets. Using the operational matrix of derivative, we reduce the problem to a set of algebraic linear equations. Some numerical example is included to demonstrate the validity and applicability of the technique. The method produces very accurate results. An estimation of error bound for this method is presented and it is shown that in this method the matrix of coefficients is a sparse matrix.
A numerical technique is presented for the solution of second order one dimensional linear hyperbolic equation. This method uses the trigonometric wavelets. The method consists of expanding the required approximate solution as the elements of trigonometric wavelets. Using the operational matrix of derivative, we reduce the problem to a set of algebraic linear equations. Some numerical example is included to demonstrate the validity and applicability of the technique. The method produces very accurate results. An estimation of error bound for this method is presented and it is shown that in this method the matrix of coefficients is a sparse matrix.
Classification : 35L20, 65L60, 65T40, 65T60
Keywords: telegraph equation; trigonometric wavelets; hermite interpolation; operational matrix of derivative 
@article{KYB_2012_48_5_a7,
     author = {Jokar, Mahmood and Lakestani, Mehrdad},
     title = {Numerical solution of second order one-dimensional linear hyperbolic equation using trigonometric wavelets},
     journal = {Kybernetika},
     pages = {939--957},
     year = {2012},
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     number = {5},
     mrnumber = {3086861},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2012_48_5_a7/}
}
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Jokar, Mahmood; Lakestani, Mehrdad. Numerical solution of second order one-dimensional linear hyperbolic equation using trigonometric wavelets. Kybernetika, Tome 48 (2012) no. 5, pp. 939-957. http://geodesic.mathdoc.fr/item/KYB_2012_48_5_a7/