Kybernetika 48 no. 5, 939-957, 2012

Numerical solution of second order one-dimensional linear hyperbolic equation using trigonometric wavelets

Mahmood Jokar and Mehrdad Lakestani


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.


telegraph equation, trigonometric wavelets, hermite interpolation, operational matrix of derivative


65T60, 65T40, 65L60, 35L20


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