Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Embedded error estimation and adaptive step-size control for optimal
  explicit strong stability preserving Runge--Kutta methods   We construct a family of embedded pairs for optimal strong stability
preserving explicit Runge-Kutta methods of order $2 \leq p \leq 4$ to be used
to obtain numerical solution of spatially discretized hyperbolic PDEs. In this
construction, the goals include non-defective methods, large region of absolute
stability, and optimal error measurement as defined in [5,19]. The new family
of embedded pairs offer the ability for strong stability preserving (SSP)
methods to adapt by varying the step-size based on the local error estimation
while maintaining their inherent nonlinear stability properties. Through
several numerical experiments, we assess the overall effectiveness in terms of
precision versus work while also taking into consideration accuracy and
stability.

35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con