Haar wavelets method for solving Pocklington's integral equation

M. Shamsi; Mohsen Razzaghi; J. Nazarzadeh; Masoud Shafiee

Kybernetika (2004)

  • Volume: 40, Issue: 4, page [491]-500
  • ISSN: 0023-5954

Abstract

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A simple and effective method based on Haar wavelets is proposed for the solution of Pocklington’s integral equation. The properties of Haar wavelets are first given. These wavelets are utilized to reduce the solution of Pocklington’s integral equation to the solution of algebraic equations. In order to save memory and computation time, we apply a threshold procedure to obtain sparse algebraic equations. Through numerical examples, performance of the present method is investigated concerning the convergence and the sparseness of resulted matrix equation.

How to cite

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Shamsi, M., et al. "Haar wavelets method for solving Pocklington's integral equation." Kybernetika 40.4 (2004): [491]-500. <http://eudml.org/doc/33714>.

@article{Shamsi2004,
abstract = {A simple and effective method based on Haar wavelets is proposed for the solution of Pocklington’s integral equation. The properties of Haar wavelets are first given. These wavelets are utilized to reduce the solution of Pocklington’s integral equation to the solution of algebraic equations. In order to save memory and computation time, we apply a threshold procedure to obtain sparse algebraic equations. Through numerical examples, performance of the present method is investigated concerning the convergence and the sparseness of resulted matrix equation.},
author = {Shamsi, M., Razzaghi, Mohsen, Nazarzadeh, J., Shafiee, Masoud},
journal = {Kybernetika},
keywords = {Pocklington integral equation; numerical solutions; Haar wavelets; Pocklington integral equation; Haar wavelets; sparse algebraic equations; numerical examples; convergence},
language = {eng},
number = {4},
pages = {[491]-500},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Haar wavelets method for solving Pocklington's integral equation},
url = {http://eudml.org/doc/33714},
volume = {40},
year = {2004},
}

TY - JOUR
AU - Shamsi, M.
AU - Razzaghi, Mohsen
AU - Nazarzadeh, J.
AU - Shafiee, Masoud
TI - Haar wavelets method for solving Pocklington's integral equation
JO - Kybernetika
PY - 2004
PB - Institute of Information Theory and Automation AS CR
VL - 40
IS - 4
SP - [491]
EP - 500
AB - A simple and effective method based on Haar wavelets is proposed for the solution of Pocklington’s integral equation. The properties of Haar wavelets are first given. These wavelets are utilized to reduce the solution of Pocklington’s integral equation to the solution of algebraic equations. In order to save memory and computation time, we apply a threshold procedure to obtain sparse algebraic equations. Through numerical examples, performance of the present method is investigated concerning the convergence and the sparseness of resulted matrix equation.
LA - eng
KW - Pocklington integral equation; numerical solutions; Haar wavelets; Pocklington integral equation; Haar wavelets; sparse algebraic equations; numerical examples; convergence
UR - http://eudml.org/doc/33714
ER -

References

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  7. Herve A., 10.1006/acha.1994.1017, Application to dyadic interpolation. Comput. Harmonic Anal. 1 (1994), 299–315 (1994) Zbl0814.42017MR1310654DOI10.1006/acha.1994.1017
  8. Pocklington H. C., Electrical oscillation in wires, Proc. Cambridge Phil. Soc. 9 (1897), 324–332 
  9. Richmond J. H., Digital computer solutions of the rigorous equations for scatter problems, Proc. IEEE 53 (1965), 796–804 (1965) 
  10. Werner D. H., Werner P. L., Breakall J. K., 10.1109/8.286230, IEEE Trans. Antennas and Propagation 42 (1994), 4, 561–563 (1994) DOI10.1109/8.286230

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