@Article{JCM-37-1,
author = {Mario, Annunziato and Messina, Eleonora},
title = {A Positive and Monotone Numerical Scheme for Volterra-Renewal Equations with Space Fluxes},
journal = {Journal of Computational Mathematics},
year = {2019},
volume = {37},
number = {1},
pages = {33--47},
abstract = {<p style="text-align: justify;">We study a numerical method for solving a system of Volterra-renewal integral equations
with space fluxes, that represents the Chapman-Kolmogorov equation for a class of
piecewise deterministic stochastic processes. The solution of this equation is related to
the time dependent distribution function of the stochastic process and it is a non-negative
and non-decreasing function of the space. Based on the Bernstein polynomials, we build
up and prove a non-negative and non-decreasing numerical method to solve that equation,
with quadratic convergence order in space.</p>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.1708-m2017-0015},
url = {https://global-sci.com/article/84380/a-positive-and-monotone-numerical-scheme-for-volterra-renewal-equations-with-space-fluxes}
}