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Engineering with Computers
Published in: Engineering with Computers 1/2021

28-06-2019 | Original Article

The approximate solution of charged particle motion equations in oscillating magnetic fields using the local multiquadrics collocation method

Authors: Pouria Assari, Fatemeh Asadi-Mehregan

Published in: Engineering with Computers | Issue 1/2021

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Abstract

The charged particle motion for certain configurations of oscillating magnetic fields can be simulated by a Volterra integro-differential equation of the second order with time-periodic coefficients. This paper investigates a simple and accurate scheme for computationally solving these types of integro-differential equations. To start the method, we first reduce the integro-differential equations to equivalent Volterra integral equations of the second kind. Subsequently, the solution of the mentioned Volterra integral equations is estimated by the collocation method based on the local multiquadrics formulated on scattered points. We also expand the proposed method to solve fractional integro-differential equations including non-integer order derivatives. Since the offered method does not need any mesh generations on the solution domain, it can be recognized as a meshless method. To demonstrate the reliability and efficiency of the new technique, several illustrative examples are given. Moreover, the numerical results confirm that the method developed in the current paper in comparison with the method based on the globally supported multiquadrics has much lesser volume computing.
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Metadata
Title
The approximate solution of charged particle motion equations in oscillating magnetic fields using the local multiquadrics collocation method
Authors
Pouria Assari
Fatemeh Asadi-Mehregan
Publication date
28-06-2019
Publisher
Springer London
Published in
Engineering with Computers / Issue 1/2021
Print ISSN: 0177-0667
Electronic ISSN: 1435-5663
DOI
https://doi.org/10.1007/s00366-019-00807-z

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