Geodesic
The convergence and accuracy of the method of macroparticles
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 19 (1979) no. 3, pp. 665-674

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The accuracy of the method of macroparticles for the Child-Langmuir problem is investigated. It is shown that the difference the self-consistent electrostatic field obtained from the discrete model and the self-consistent electrostatic field of the kinetic model is $O(N^{1/2})$. 
@article{ZVMMF_1979_19_3_a9,
     author = {Yu. I. Mokin},
     title = {The convergence and accuracy of the method of macroparticles},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {665--674},
     publisher = {mathdoc},
     volume = {19},
     number = {3},
     year = {1979},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_1979_19_3_a9/}
}
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Yu. I. Mokin. The convergence and accuracy of the method of macroparticles. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 19 (1979) no. 3, pp. 665-674. http://geodesic.mathdoc.fr/item/ZVMMF_1979_19_3_a9/