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Galerkin approximations for the one‐dimensional vlasov‐poisson equation
Author(s) -
Cooper J.,
Neunzert H.
Publication year - 1983
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670050131
Subject(s) - mathematics , galerkin method , vlasov equation , mathematical analysis , space (punctuation) , variable (mathematics) , discrete poisson equation , series (stratigraphy) , poisson's equation , scheme (mathematics) , poisson distribution , partial differential equation , finite element method , laplace's equation , plasma , physics , quantum mechanics , paleontology , linguistics , biology , thermodynamics , statistics , philosophy
By taking Fourier series in the space variable, and truncating, we construct a Galerkin scheme for approximate solutions to the one dimensional Vlasov‐Poisson equation. Existence is proved for the approximate solutions and they are shown to converge to an exact solution in a weak sense.