# On the approximate solution of integro-differential equations arising in oscillating magnetic fields

K. Maleknejad; M. Hadizadeh; M. Attary

Applications of Mathematics (2013)

- Volume: 58, Issue: 5, page 595-607
- ISSN: 0862-7940

## Access Full Article

top## Abstract

top## How to cite

topMaleknejad, K., Hadizadeh, M., and Attary, M.. "On the approximate solution of integro-differential equations arising in oscillating magnetic fields." Applications of Mathematics 58.5 (2013): 595-607. <http://eudml.org/doc/260647>.

@article{Maleknejad2013,

abstract = {In this work, we propose the Shannon wavelets approximation for the numerical solution of a class of integro-differential equations which describe the charged particle motion for certain configurations of oscillating magnetic fields. We show that using the Galerkin method and the connection coefficients of the Shannon wavelets, the problem is transformed to an infinite algebraic system, which can be solved by fixing a finite scale of approximation. The error analysis of the method is also investigated. Finally, some numerical experiments are reported to illustrate the accuracy and applicability of the method.},

author = {Maleknejad, K., Hadizadeh, M., Attary, M.},

journal = {Applications of Mathematics},

keywords = {charged particle motion; oscillating magnetic field; integro-differential equation; Shannon wavelet; numerical treatment; charged particle motion; oscillating magnetic field; integro-differential equation; Shannon wavelet; numerical treatment},

language = {eng},

number = {5},

pages = {595-607},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {On the approximate solution of integro-differential equations arising in oscillating magnetic fields},

url = {http://eudml.org/doc/260647},

volume = {58},

year = {2013},

}

TY - JOUR

AU - Maleknejad, K.

AU - Hadizadeh, M.

AU - Attary, M.

TI - On the approximate solution of integro-differential equations arising in oscillating magnetic fields

JO - Applications of Mathematics

PY - 2013

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 58

IS - 5

SP - 595

EP - 607

AB - In this work, we propose the Shannon wavelets approximation for the numerical solution of a class of integro-differential equations which describe the charged particle motion for certain configurations of oscillating magnetic fields. We show that using the Galerkin method and the connection coefficients of the Shannon wavelets, the problem is transformed to an infinite algebraic system, which can be solved by fixing a finite scale of approximation. The error analysis of the method is also investigated. Finally, some numerical experiments are reported to illustrate the accuracy and applicability of the method.

LA - eng

KW - charged particle motion; oscillating magnetic field; integro-differential equation; Shannon wavelet; numerical treatment; charged particle motion; oscillating magnetic field; integro-differential equation; Shannon wavelet; numerical treatment

UR - http://eudml.org/doc/260647

ER -

## References

top- Agarwal, R. P., Boundary Value Problems for Higher Order Differential Equations, World Scientific Singapore (1986). (1986) Zbl0619.34019MR1021979
- Akyüz-Daşcioğlu, A., 10.1016/S0096-3003(03)00334-5, Appl. Math. Comput. 151 (2004), 221-232. (2004) Zbl1049.65149MR2037962DOI10.1016/S0096-3003(03)00334-5
- Akyüz-Daşcioğlu, A., Sezer, M., 10.1016/j.jfranklin.2005.04.001, J. Franklin Inst. 342 (2005), 688-701. (2005) Zbl1086.65121MR2166749DOI10.1016/j.jfranklin.2005.04.001
- Bojeldain, A. A., On the numerical solving of nonlinear Volterra integro-differential equations, Ann. Univ. Sci. Budap. Rolando Eötvös, Sect. Comput. 11 (1991), 105-125. (1991) Zbl0755.45011MR1158315
- Brunner, H., Makroglou, A., Miller, R. K., 10.1016/S0168-9274(96)00075-X, Appl. Numer. Math. 23 (1997), 381-402. (1997) Zbl0876.65090MR1453423DOI10.1016/S0168-9274(96)00075-X
- Cattani, C., Connection coefficients of Shannon wavelets, Math. Model. Anal. 11 (2006), 117-132. (2006) Zbl1117.65179MR2231204
- Cattani, C., Shannon wavelets for the solution of integrodifferential equations, Math. Probl. Eng. (2010), Article ID 408418. (2010) Zbl1191.65174MR2610514
- Dehghan, M., Shakeri, F., 10.2528/PIER07090403, Progress In Electromagnetics Research 78 (2008), 361-376. (2008) DOI10.2528/PIER07090403
- Domke, K., Hacia, L., Integral equations in some thermal problems, Int. J. Math. Comput. Simulation 2 (2007), 184-189. (2007)
- Machado, J. M., Tsuchida, M., Solutions for a class of integro-differential equations with time periodic coefficients, Appl. Math. E-Notes 2 (2002), 66-71. (2002) Zbl0999.45003MR1979412
- Maleknejad, K., Attary, M., 10.1016/j.cnsns.2010.09.037, Commun. Nonlinear Sci. Numer. Simul. 16 (2011), 2672-2679. (2011) Zbl1221.65332MR2772283DOI10.1016/j.cnsns.2010.09.037
- Mureşan, V., 10.4171/ZAA/1194, Z. Anal. Anwend. 23 (2004), 205-216. (2004) Zbl1062.45006MR2066102DOI10.4171/ZAA/1194
- Wu, G.-C., Lee, E. W. M., 10.1016/j.physleta.2010.04.034, Phys. Lett., A 374 (2010), 2506-2509. (2010) Zbl1237.34007MR2640023DOI10.1016/j.physleta.2010.04.034
- Yildirim, A., 10.1016/j.camwa.2008.07.020, Comput. Math. Appl. 56 (2008), 3175-3180. (2008) Zbl1165.65377MR2474572DOI10.1016/j.camwa.2008.07.020

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.