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

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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

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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

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  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
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