Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An explicit numerical algorithm to the solution of Volterra integral
  equation of the second kind   This paper considers a numeric algorithm to solve the equation \begin{align*}
y(t)=f(t)+\int^t_0 g(t-\tau)y(\tau)\,d\tau \end{align*} with a kernel $g$ and
input $f$ for $y$. In some applications we have a smooth integrable kernel but
the input $f$ could be a generalised function, which could involve the Dirac
distribution. We call the case when $f=\delta$, the Dirac distribution centred
at 0, the fundamental solution $E$, and show that $E=\delta+h$ where $h$ is
integrable and solve \begin{align*} h(t)=g(t)+\int^t_0 g(t-\tau)h(\tau)\,d\tau
\end{align*} The solution of the general case is then \begin{align*}
y(t)=f(t)+(h*f)(t) \end{align*} which involves the convolution of $h$ and $f$.
We can approximate $g$ to desired accuracy with piecewise constant kernel for
which the solution $h$ is known explicitly. We supply an algorithm for the
solution of the integral equation with specified accuracy.

8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
27
The categories of this paper are: comp-gas