Geodesic
Haar wavelets method for solving Pocklington's integral equation
Kybernetika, Tome 40 (2004) no. 4, pp. 491-500 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 45H05, 65R20, 65T60, 78M25
Keywords: Pocklington integral equation; numerical solutions; Haar wavelets 
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     title = {Haar wavelets method for solving {Pocklington's} integral equation},
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Shamsi, M.; Razzaghi, M.; Nazarzadeh, J.; Shafiee, M. Haar wavelets method for solving Pocklington's integral equation. Kybernetika, Tome 40 (2004) no. 4, pp. 491-500. http://geodesic.mathdoc.fr/item/KYB_2004_40_4_a6/

[1] Beylkin G., Coifman, R., Rokhlin V.: Fast wavelet transforms and numerical algorithms, I. Commun. Pure Appl. Math. 44 (1991), 141–183 | DOI | MR | Zbl

[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 | DOI | MR

[3] Daubechies I.: The wavelet transform, time-frequency localization and signal analysis. IEEE Trans. Inform. Theory 36 (1990), 961–1005 | DOI | MR | Zbl

[4] Daubechies I.: Ten Lectures on Wavelets. SIAM, 1992 | MR | Zbl

[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 | DOI | MR

[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 | DOI | MR | Zbl

[7] Herve A.: Multi-resolution analysis of multiplicity $d$. Application to dyadic interpolation. Comput. Harmonic Anal. 1 (1994), 299–315 | DOI | MR | Zbl

[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

[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 | DOI