Fast Algorithm for Numerically Integrating Equations of Motion
for Large Particles in Microwave Devices

A. A. Kuraev^{a, b}, A. O. Rak^a, S. V. Kolosov^a, A. A. Koronovskii^{b, c}, and A. E. Hramov^{b, c}*

^a Belarusian State University of Informatics and Radioelectronics, ul. P. Brovki 6, Minsk, 220013 Belarus
^b Chernyshevsky State University, Bol’shaya Kazach’ya ul. 112, Saratov, 410012 Russia
^c Gagarin State Technical University, Politekhnicheskaya ul. 77, Saratov, 410054 Russia
*e-mail: hramovae@gmail.com

Received April 23, 2013

Abstract—An algorithm for numerically integrating the equations of motion for large particles is formulated.
The algorithm is represented in three forms—an explicit form, a predictor—corrector form, and a modified
form that is intended for simulating the motion of relativistic particles in an electromagnetic field. The order of
precision of the proposed algorithm is analyzed. The results of a comparison with standard algorithms are pre-
sented. The efficiency of this algorithm is demonstrated in considering the test example of a harmonic oscillator
and in numerically simulating the Pierce diode in the mode of virtual-cathode formation.

DOI: 10.1134/S1063784214030165

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