Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Convergence analysis of multi-level spectral deferred corrections   The spectral deferred correction (SDC) method is class of iterative solvers
for ordinary differential equations (ODEs). It can be interpreted as a
preconditioned Picard iteration for the collocation problem. The convergence of
this method is well-known, for suitable problems it gains one order per
iteration up to the order of the quadrature method of the collocation problem
provided. This appealing feature enables an easy creation of flexible,
high-order accurate methods for ODEs. A variation of SDC are multi-level
spectral deferred corrections (MLSDC). Here, iterations are performed on a
hierarchy of levels and an FAS correction term, as in nonlinear multigrid
methods, couples solutions on different levels. While there are several
numerical examples which show its capabilities and efficiency, a theoretical
convergence proof is still missing. This paper addresses this issue. A proof of
the convergence of MLSDC, including the determination of the convergence rate
in the time-step size, will be given and the results of the theoretical
analysis will be numerically demonstrated. It turns out that there are
restrictions for the advantages of this method over SDC regarding the
convergence rate.

17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th