Previous |  Up |  Next


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:
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


Files Size Format View
Kybernetika_40-2004-4_7.pdf 1.125Mb application/pdf View/Open
Back to standard record
Partner of
EuDML logo