Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Newton Type Methods for solving a Hasegawa-Mima Plasma Model   In [1], the non-linear space-time Hasegawa-Mima plasma equation is formulated
as a coupled system of two linear PDE's, a solution of which is a pair (u, w).
The first equation is of hyperbolic type and the second of elliptic type.
Variational frames for obtaining weak solutions to the initial value
Hasegawa-Mima problem with periodic boundary conditions were also derived. In a
more recent work [2], a numerical approach consisting of a finite element
space-domain combined with an Euler-implicit time scheme was used to discretize
the coupled variational Hasegawa-Mima model. A semi-linear version of this
implicit nonlinear scheme was tested for several types of initial conditions.
This semi-linear scheme proved to lack efficiency for long time, which
necessitates imposing a cap on the magnitude of the solution. To circumvent
this difficulty, in this paper, we use Newton-type methods (Newton, Chord and
an introduced Modified Newton method) to solve numerically the fully-implicit
non-linear scheme. Testing these methods in FreeFEM++ indicates significant
improvements as no cap needs to be imposed for long time. In the sequel, we
demonstrate the validity of these methods by proving several results, in
particular the convergence of the implemented methods.

32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an