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

Abstract

top
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.

How to cite

top

Maleknejad, 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
  1. Agarwal, R. P., Boundary Value Problems for Higher Order Differential Equations, World Scientific Singapore (1986). (1986) Zbl0619.34019MR1021979
  2. 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
  3. 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
  4. 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
  5. 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
  6. Cattani, C., 10.3846/13926292.2006.9637307, Math. Model. Anal. 11 (2006), 117-132. (2006) Zbl1117.65179MR2231204DOI10.3846/13926292.2006.9637307
  7. Cattani, C., Shannon wavelets for the solution of integrodifferential equations, Math. Probl. Eng. (2010), Article ID 408418. (2010) Zbl1191.65174MR2610514
  8. Dehghan, M., Shakeri, F., 10.2528/PIER07090403, Progress In Electromagnetics Research 78 (2008), 361-376. (2008) DOI10.2528/PIER07090403
  9. Domke, K., Hacia, L., Integral equations in some thermal problems, Int. J. Math. Comput. Simulation 2 (2007), 184-189. (2007) 
  10. 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
  11. 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
  12. Mureşan, V., 10.4171/ZAA/1194, Z. Anal. Anwend. 23 (2004), 205-216. (2004) Zbl1062.45006MR2066102DOI10.4171/ZAA/1194
  13. 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
  14. 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 ?

top

You must be logged in to post comments.

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

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.