Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Explicit exponential Runge-Kutta methods of high order for parabolic
  problems   Exponential Runge-Kutta methods constitute efficient integrators for
semilinear stiff problems. So far, however, explicit exponential Runge-Kutta
methods are available in the literature up to order 4 only. The aim of this
paper is to construct a fifth-order method. For this purpose, we make use of a
novel approach to derive the stiff order conditions for high-order exponential
methods. This allows us to obtain the conditions for a method of order 5 in an
elegant way. After stating the conditions, we first show that there does not
exist an explicit exponential Runge-Kutta method of order 5 with less than or
equal to 6 stages. Then, we construct a fifth-order method with 8 stages and
prove its convergence for semilinear parabolic problems. Finally, a numerical
example is given that illustrates our convergence bound.

31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
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The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio