Geodesic
On the approximate solution of integro-differential equations arising in oscillating magnetic fields
Applications of Mathematics, Tome 58 (2013) no. 5, pp. 595-607 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
DOI : 10.1007/s10492-013-0029-z
Classification : 34B05, 34K28, 78A35
Keywords: charged particle motion; oscillating magnetic field; integro-differential equation; Shannon wavelet; numerical treatment 
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     title = {On the approximate solution of integro-differential equations arising in oscillating magnetic fields},
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Maleknejad, K.; Hadizadeh, M.; Attary, M. On the approximate solution of integro-differential equations arising in oscillating magnetic fields. Applications of Mathematics, Tome 58 (2013) no. 5, pp. 595-607. doi: 10.1007/s10492-013-0029-z

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