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

Mahmood Jokar; Mehrdad Lakestani

Kybernetika (2012)

  • Volume: 48, Issue: 5, page 939-957
  • ISSN: 0023-5954

Abstract

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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.

How to cite

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Jokar, Mahmood, and Lakestani, Mehrdad. "Numerical solution of second order one-dimensional linear hyperbolic equation using trigonometric wavelets." Kybernetika 48.5 (2012): 939-957. <http://eudml.org/doc/251373>.

@article{Jokar2012,
abstract = {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.},
author = {Jokar, Mahmood, Lakestani, Mehrdad},
journal = {Kybernetika},
keywords = {telegraph equation; trigonometric wavelets; hermite interpolation; operational matrix of derivative; telegraph equation; trigonometric wavelets; Hermite interpolation; operational matrix of derivative; convergence; Galerkin method; numerical example; error bound},
language = {eng},
number = {5},
pages = {939-957},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Numerical solution of second order one-dimensional linear hyperbolic equation using trigonometric wavelets},
url = {http://eudml.org/doc/251373},
volume = {48},
year = {2012},
}

TY - JOUR
AU - Jokar, Mahmood
AU - Lakestani, Mehrdad
TI - Numerical solution of second order one-dimensional linear hyperbolic equation using trigonometric wavelets
JO - Kybernetika
PY - 2012
PB - Institute of Information Theory and Automation AS CR
VL - 48
IS - 5
SP - 939
EP - 957
AB - 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.
LA - eng
KW - telegraph equation; trigonometric wavelets; hermite interpolation; operational matrix of derivative; telegraph equation; trigonometric wavelets; Hermite interpolation; operational matrix of derivative; convergence; Galerkin method; numerical example; error bound
UR - http://eudml.org/doc/251373
ER -

References

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