Title:
|
Haar wavelets method for solving Pocklington's integral equation (English) |
Author:
|
Shamsi, M. |
Author:
|
Razzaghi, M. |
Author:
|
Nazarzadeh, J. |
Author:
|
Shafiee, M. |
Language:
|
English |
Journal:
|
Kybernetika |
ISSN:
|
0023-5954 |
Volume:
|
40 |
Issue:
|
4 |
Year:
|
2004 |
Pages:
|
[491]-500 |
Summary lang:
|
English |
. |
Category:
|
math |
. |
Summary:
|
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. (English) |
Keyword:
|
Pocklington integral equation |
Keyword:
|
numerical solutions |
Keyword:
|
Haar wavelets |
MSC:
|
45H05 |
MSC:
|
65R20 |
MSC:
|
65T60 |
MSC:
|
78M25 |
idZBL:
|
Zbl 1249.65289 |
idMR:
|
MR2102367 |
. |
Date available:
|
2009-09-24T20:03:07Z |
Last updated:
|
2015-03-23 |
Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135610 |
. |
Reference:
|
[1] Beylkin G., Coifman, R., Rokhlin V.: Fast wavelet transforms and numerical algorithms, I.Commun. Pure Appl. Math. 44 (1991), 141–183 Zbl 0722.65022, MR 1085827, 10.1002/cpa.3160440202 |
Reference:
|
[2] Dahmen W. S. Proessdorf , Schneider R.: Wavelet approximation methods for pseudodifferential equations II: Matrix compression and fast algorithms.Adv. in Comput. Math. 1 (1993), 259–335 MR 1242378, 10.1007/BF02072014 |
Reference:
|
[3] Daubechies I.: The wavelet transform, time-frequency localization and signal analysis.IEEE Trans. Inform. Theory 36 (1990), 961–1005 Zbl 0738.94004, MR 1066587, 10.1109/18.57199 |
Reference:
|
[4] Daubechies I.: Ten Lectures on Wavelets.SIAM, 1992 Zbl 1006.42030, MR 1162107 |
Reference:
|
[5] Davies P. J., Duncan D. B., Funkenz S. A.: Accurate and efficient algorithms for frequency domain scattering from a thin wire.J. Comput. Phys. 168 (2001), 1, 155-183 MR 1826912, 10.1006/jcph.2000.6688 |
Reference:
|
[6] Goswami J. C., Chan A. K., Chui C. K.: On solving first-kind integral equations using wavelets on a bounded interval.IEEE Trans. Antennas and Propagation 43 (1995), 6, 614–622 Zbl 0944.65537, MR 1333075, 10.1109/8.387178 |
Reference:
|
[7] Herve A.: Multi-resolution analysis of multiplicity $d$.Application to dyadic interpolation. Comput. Harmonic Anal. 1 (1994), 299–315 Zbl 0814.42017, MR 1310654, 10.1006/acha.1994.1017 |
Reference:
|
[8] Pocklington H. C.: Electrical oscillation in wires.Proc. Cambridge Phil. Soc. 9 (1897), 324–332 |
Reference:
|
[9] Richmond J. H.: Digital computer solutions of the rigorous equations for scatter problems.Proc. IEEE 53 (1965), 796–804 |
Reference:
|
[10] Werner D. H., Werner P. L., Breakall J. K.: Some computational aspects of Pocklington’s integral equation for thin wires.IEEE Trans. Antennas and Propagation 42 (1994), 4, 561–563 10.1109/8.286230 |
. |