Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An adaptive step size controller for iterative implicit methods   The automatic selection of an appropriate time step size has been considered
extensively in the literature. However, most of the strategies developed
operate under the assumption that the computational cost (per time step) is
independent of the step size. This assumption is reasonable for non-stiff
ordinary differential equations and for partial differential equations where
the linear systems of equations resulting from an implicit integrator are
solved by direct methods. It is, however, usually not satisfied if iterative
(for example, Krylov) methods are used.
  In this paper, we propose a step size selection strategy that adaptively
reduces the computational cost (per unit time step) as the simulation
progresses, constraint by the tolerance specified. We show that the proposed
approach yields significant improvements in performance for a range of problems
(diffusion-advection equation, Burgers' equation with a reaction term, porous
media equation, viscous Burgers' equation, Allen--Cahn equation, and the
two-dimensional Brusselator system). While traditional step size controllers
have emphasized a smooth sequence of time step sizes, we emphasize the
exploration of different step sizes which necessitates relatively rapid changes
in the step size.

4
The categories of this paper are: cond-mat
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys