Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A novel *R-based perspective on solving ordinary differential equations   The real numbers, it is taught at universities, correspond to our idea of a
continuum, although the hyperreal numbers are located ``in between'' the real
numbers. The number $x + dx$, where $dx$ should be an infinitesimal number and
$x$ real, is infinitesimally close to $x$ but ``infinitely'' far away from all
other real numbers. Analogously: If $f'(x_0)$ and $f(x_0)$ are given for a
differentiable function $f:\mathbb{R}\rightarrow\mathbb{R}$ at
$x_0\in\mathbb{R}$, we can not determine $f(x)$ at {\em any} point $x\in
\mathbb{R}$ different from $x_0$. These points seem to be ``infinitely'' far
away. That is one conceptual problem of solving differential equations in
numerical mathematics. In this article, we will present a numerical algorithm
to solve very simple initial value problems. However, the change of paradigm
is, that we will not ``leave'' the point $x_0$. Solving ordinary differential
equations is like searching for ``recipes'' $f$. Instead of trying to find
these recipes for values $x\in\mathbb{R}$, we will learn them from special
relations in the ``monad'' of $x_0$.

10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
14
The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph