Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A numerical framework for computing steady states of size-structured
  population models and their stability   Structured population models are a class of general evolution equations which
are widely used in the study of biological systems. Many theoretical methods
are available for establishing existence and stability of steady states of
general evolution equations. However, except for very special cases, finding an
analytical form of stationary solutions for evolution equations is a
challenging task. In the present paper, we develop a numerical framework for
computing approximations to stationary solutions of general evolution
equations, which can also be used to produce existence and stability regions
for steady states. In particular, we use the Trotter-Kato Theorem to
approximate the infinitesimal generator of an evolution equation on a finite
dimensional space, which in turn reduces the evolution equation into a system
of ordinary differential equations. Consequently, we approximate and study the
asymptotic behavior of stationary solutions. We illustrate the convergence of
our numerical framework by applying it to a linear Sinko-Streifer structured
population model for which the exact form of the steady state is known. To
further illustrate the utility of our approach, we apply our framework to
nonlinear population balance equation, which is an extension of well-known
Smoluchowksi coagulation-fragmentation model to biological populations. We also
demonstrate that our numerical framework can be used to gain insight about the
theoretical stability of the stationary solutions of the evolution equations.
Furthermore, the open source Python program that we have developed for our
numerical simulations is freely available from our Github repository
(github.com/MathBioCU).

18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
13
The categories of this paper are: quant-ph