Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weighted and shifted BDF2 methods on variable grids   Variable steps implicit-explicit multistep methods for PDEs have been
presented in [17], where the zero-stability is studied for ODEs; however, the
stability analysis still remains an open question for PDEs. Based on the idea
of linear multistep methods, we present a simple weighted and shifted BDF2
methods with variable steps for the parabolic problems, which serve as a bridge
between BDF2 and Crank-Nicolson scheme. The contributions of this paper are as
follows: we first prove that the optimal adjacent time-step ratios for the
weighted and shifted BDF2, which greatly improve the maximum time-step ratios
for BDF2 in [11,15]. Moreover, the unconditional stability and optimal
convergence are rigorous proved, which make up for the vacancy of the theory
for PDEs in [17]. Finally, numerical experiments are given to illustrate
theoretical results.

33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio