Construction of Positivity Preserving Full-Discrete Scheme for Stochastic Age-Structured Population Equations

Wenjuan Wang

doi:https://doi.org/10.14445/22315373/IJMTT-V68I10P504

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 68 | Issue 10 | Year 2022 | Article Id. IJMTT-V68I10P504 | DOI : https://doi.org/10.14445/22315373/IJMTT-V68I10P504

Construction of Positivity Preserving Full-Discrete Scheme for Stochastic Age-Structured Population Equations

Wenjuan Wang

Received	Revised	Accepted	Published
28 Aug 2022	06 Oct 2022	17 Oct 2022	28 Oct 2022

Citation :

Wenjuan Wang, "Construction of Positivity Preserving Full-Discrete Scheme for Stochastic Age-Structured Population Equations," International Journal of Mathematics Trends and Technology (IJMTT), vol. 68, no. 10, pp. 20-27, 2022. Crossref, https://doi.org/10.14445/22315373/IJMTT-V68I10P504

Abstract

The numerical solutions of the stochastic age-structured population models may appear negative when the disturbance intensity is sufficiently large. This phenomenon goes against the biological meaning and people’s cognition, but it is indeed the case. In order to circumvent this unreasonable situation, this paper aims to construct a full-discrete positivepreserving numerical scheme for stochastic age-structured population models. The technique we use is based on the balanced implicit method (BIM), a relatively mature tool that plays a crucial role in the issue of keeping positivity. Also，we proved the convergence of new numerical scheme we obtained, the strong convergence order is 1/2. At last, several numerical experiments are given to verify the accuracy of theoretical results.

Keywords

Stochastic age-structured population equations, Balanced implicit method, Numerical solution, Positivity preserving, Convergence.

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