Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the numerical solution of some nonlinear stochastic differential
  equations using the semi-discrete method   In this paper we are interested in the numerical solution of stochastic
differential equations with non negative solutions. Our goal is to construct
explicit numerical schemes that preserve positivity, even for super linear
stochastic differential equations. It is well known that the usual Euler scheme
diverges on super linear problems and the Tamed-Euler method does not preserve
positivity. In that direction, we use the Semi-Discrete method that the first
author has proposed in two previous papers. We propose a new numerical scheme
for a class of stochastic differential equations which are super linear with
non negative solution. In this class of stochastic differential equations
belongs the Heston $3/2$-model that appears in financial mathematics, for which
we prove %theoretically and through numerical experiments the "optimal" order
of strong convergence at least $1/2$ of the Semi-Discrete method.

33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int