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Volume 37, Issue 1
A Positive and Monotone Numerical Scheme for Volterra-Renewal Equations with Space Fluxes

Mario Annunziato & Eleonora Messina

DOI: 10.4208/jcm.1708-m2017-0015

J. Comp. Math., 37 (2019), pp. 33-47.

Published online: 2018-08

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  • Abstract

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.

  • Keywords

Volterra renewal, Piecewise deterministic process, Monotone positive numerical scheme, Bernstein polynomials.

  • AMS Subject Headings

65R20, 45D05, 45M20

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

mannunzi@unisa.it (Mario Annunziato)

eleonora.messina@unina.it (Eleonora Messina)

  • BibTex
  • RIS
  • TXT
@Article{JCM-37-33, author = {Annunziato , Mario and Messina , Eleonora}, title = {A Positive and Monotone Numerical Scheme for Volterra-Renewal Equations with Space Fluxes}, journal = {Journal of Computational Mathematics}, year = {2018}, volume = {37}, number = {1}, pages = {33--47}, abstract = {

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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1708-m2017-0015}, url = {http://global-sci.org/intro/article_detail/jcm/12647.html} }
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 -

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.

Annunziato , Mario and Messina , Eleonora. (2018). A Positive and Monotone Numerical Scheme for Volterra-Renewal Equations with Space Fluxes. Journal of Computational Mathematics. 37 (1). 33-47. doi:10.4208/jcm.1708-m2017-0015
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