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The central purpose of this thesis is to explore the behavior of the numerical solution of the Cold- Ion model with shock forming conditions in one and two dimensions. In the one dimensional case, a comparison between the numerical solution of the Vlasov equation is made. It is observed that the Cold-Ion model is no longer representative of the cold-ion limit of the Vlasov-Poisson equation when a spike forms in the solution. It was found that the lack of a spike in the solution of the Cold-Ion model does not necessarily mean that a bifurcation has not formed in the solution of the Vlasov-Poisson equation. It was also determined that the spike present in the solution of the one dimensional problem appears again in the two dimensional simulation. The findings presented in this thesis opens up the question of determining which initial and boundary conditions of the Cold-Ion model causes a shock to form in the solution.
A Thesis submitted to the Department of Scientiﬁc Computing in partial fulfillment of the requirements for the degree of Master of Science.
Includes bibliographical references.
Max Gunzburger, Professor Directing Thesis; Janet Peterson, Committee Member; Sachin Shanbhag, Committee Member.
Florida State University
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