The power series in time of the solution to the one-dimensional Vlasov-Poisson equation

Authors

Jose Perico H. Esguerra ⋅ PH National Institute of Physics, University of the Philippines Diliman
Pecier C. Decierdo ⋅ PH National Institute of Physics, University of the Philippines Diliman

Abstract

A small time solution method for the one-dimensional Vlasov-Poisson equation through expanding the solution as a power series in time and calculating the coefficients is here presented. The coefficients in this power series, which are functions of the space variable x and the speed v, are obtained using a recursion relation. The fourth-order approximation is calculated and is compared with the first-order approximate solution obtained using the method of characteristics, both evaluated at very small time scales or times very close to zero (t ~ 0). By analyzing the function defined as the difference of the two functions for some given time, we conclude that for t ~ 0.01, the absolute difference between the two solutions is of order 10^-3 only. This is strong evidence that the power series expansion of the solution f in t is convergent for t<<1.

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Issue

2009: Proceedings of the 27th Samahang Pisika ng Pilipinas Physics Congress

Article ID

SPP-2009-PA-20

Section

Poster Session PA

Published

2009-10-28

How to Cite

[1]

JPH Esguerra and PC Decierdo, The power series in time of the solution to the one-dimensional Vlasov-Poisson equation, Proceedings of the Samahang Pisika ng Pilipinas 27, SPP-2009-PA-20 (2009). URL: https://proceedings.spp-online.org/article/view/SPP-2009-PA-20.