Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Conservative iterative methods for implicit discretizations of
  conservation laws   Conservation properties of iterative methods applied to implicit finite
volume discretizations of nonlinear conservation laws are analyzed. It is shown
that any consistent multistep or Runge-Kutta method is globally conservative.
Further, it is shown that Newton's method, Krylov subspace methods and
pseudo-time iterations are globally conservative while the Jacobi and
Gauss-Seidel methods are not in general. If pseudo-time iterations using an
explicit Runge-Kutta method are applied to a locally conservative
discretization, then the resulting scheme is also locally conservative.
However, the corresponding numerical flux can be inconsistent with the
conservation law. We prove an extension of the Lax-Wendroff theorem, which
reveals that numerical solutions based on these methods converge to weak
solutions of a modified conservation law where the flux function is multiplied
by a particular constant. This constant depends on the choice of Runge-Kutta
method but is independent of both the conservation law and the discretization.
Consistency is maintained by ensuring that this constant equals unity and a
strategy for achieving this is presented. Experiments show that this strategy
improves the convergence rate of the pseudo-time iterations.

28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con