Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exponential integrators for a Markov chain model of the fast sodium
  channel of cardiomyocytes   The modern Markov chain models of ionic channels in excitable membranes are
numerically stiff. The popular numerical methods for these models require very
small time steps to ensure stability. Our objective is to formulate and test
two methods addressing this issue, so that the timestep can be chosen based on
accuracy rather than stability.
  Both proposed methods extend Rush-Larsen technique, which was originally
developed to Hogdkin-Huxley type gate models. One method, "Matrix Rush-Larsen"
(MRL) uses a matrix reformulation of the Rush-Larsen scheme, where the matrix
exponentials are calculated using precomputed tables of eigenvalues and
eigenvectors. The other, "hybrid operator splitting" (HOS) method exploits
asymptotic properties of a particular Markov chain model, allowing explicit
analytical expressions for the substeps.
  We test both methods on the Clancy and Rudy (2002) INa Markov chain model.
With precomputed tables for functions of the transmembrane voltage, both
methods are comparable to the forward Euler method in accuracy and
computational cost, but allow longer time steps without numerical instability.
  We conclude that both methods are of practical interest. MRL requires more
computations than HOS, but is formulated in general terms which can be readily
extended to other Markov Chain channel models, whereas the utility of HOS
depends on the asymptotic properties of a particular model.
  The significance of the methods is that they allow a considerable speed-up of
large-scale computations of cardiac excitation models by increasing the time
step, while maintaining acceptable accuracy and preserving numerical stability.

21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ