Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Jacobian-free explicit multiderivative Runge-Kutta methods for
  hyperbolic conservation laws   Based on the recent development of Jacobian-free Lax-Wendroff (LW) approaches
for solving hyperbolic conservation laws [Zorio, Baeza and Mulet, Journal of
Scientific Computing 71:246-273, 2017], [Carrillo and Par\'es, Journal of
Scientific Computing 80:1832-1866, 2019], a novel collection of explicit
Jacobian-free multistage multiderivative solvers for hyperbolic conservation
laws is presented in this work. In contrast to Taylor time-integration methods,
multiderivative RungeKutta (MDRK) techniques achieve higher-order of
consistency not only through the excessive addition of higher temporal
derivatives, but also through the addition of Runge-Kutta-type stages. This
adds more flexibility to the time integration in such a way that more stable
and more efficient schemes could be identified. The novel method permits the
practical application of MDRK schemes. In their original form, they are
difficult to utilize as higher-order flux derivatives have to be computed
analytically. Here we overcome this by adopting a Jacobian-free approximation
of those derivatives. In this paper, we analyze the novel method with respect
to order of consistency and stability. We show that the linear CFL number
varies significantly with the number of derivatives used. Results are verified
numerically on several representative testcases.

16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th