Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Analysis of exponential splitting methods for inhomogeneous parabolic
  equations   We analyze the convergence of the exponential Lie and exponential Strang
splitting applied to inhomogeneous second-order parabolic equations with
Dirichlet boundary conditions. A recent result on the smoothing properties of
these methods allows us to prove sharp convergence results in the case of
homogeneous Dirichlet boundary conditions. When no source term is present and
natural regularity assumptions are imposed on the initial value, we show
full-order convergence of both methods. For inhomogeneous equations, we prove
full-order convergence for the exponential Lie splitting, whereas order
reduction to 1.25 for the exponential Strang splitting. Furthermore, we give
sufficient conditions on the inhomogeneity for full-order convergence of both
methods. Moreover our theoretical convergence results explain the severe order
reduction to 0.25 of splitting methods applied to problems involving
inhomogeneous Dirichlet boundary conditions. We include numerical experiments
to underline the sharpness of our theoretical convergence results.

19
The categories of this paper are: eess
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga