TY - JOUR
T1 - A Positive and Monotone Numerical Scheme for Volterra-Renewal Equations with Space Fluxes
AU - Annunziato , Mario
AU - Messina , Eleonora
JO - Journal of Computational Mathematics
VL - 1
SP - 33
EP - 47
PY - 2018
DA - 2018/08
SN - 37
DO - http://doi.org/10.4208/jcm.1708-m2017-0015
UR - https://global-sci.org/intro/article_detail/jcm/12647.html
KW - Volterra renewal, Piecewise deterministic process, Monotone positive numerical scheme, Bernstein polynomials.
AB - <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>