The thin plate spline collocation method for solving integro-differential equations arisen from the charged particle motion in oscillating magnetic fields
ISSN: 0264-4401
Article publication date: 3 July 2018
Issue publication date: 23 July 2018
Abstract
Purpose
The purpose of this study is to obtain a scheme for the numerical solution of Volterra integro-differential equations with time periodic coefficients deduced from the charged particle motion for certain configurations of oscillating magnetic fields.
Design/methodology/approach
The method reduces the solution of these types of integro-differential equations to the solution of two-dimensional Volterra integral equations of the second kind. The new method uses the discrete collocation method together with thin plate splines constructed on a set of scattered points as a basis.
Findings
The scheme can be easily implemented on a computer and has a computationally attractive algorithm. Numerical examples are included to show the validity and efficiency of the new technique.
Originality/value
The author uses thin plate splines as a type of free-shape parameter radial basis functions which establish an effective and stable method to solve electromagnetic integro-differential equations. As the scheme does not need any background meshes, it can be identified as a meshless method.
Keywords
Acknowledgements
The author is very grateful to the three anonymous reviewers for carefully reading the paper and for comments and suggestions which have improved the paper. Also, the author would like to thank Dr Vahid Kamali (Department of Physics, Bu-Ali Sina University) for his valuable remarks.
Citation
Assari, P. (2018), "The thin plate spline collocation method for solving integro-differential equations arisen from the charged particle motion in oscillating magnetic fields", Engineering Computations, Vol. 35 No. 4, pp. 1706-1726. https://doi.org/10.1108/EC-08-2017-0330
Publisher
:Emerald Publishing Limited
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