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A new convergence and positivity analysis of balanced Euler method for stochastic age‐dependent population equations
Author(s) -
Tan Jianguo,
Mayavel Pichamuthu,
Rathinasamy Anandaraman,
Cao Honglei
Publication year - 2021
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22606
Subject(s) - mathematics , convergence (economics) , euler's formula , numerical analysis , backward euler method , population , euler equations , euler method , order (exchange) , mathematical analysis , demography , sociology , economics , economic growth , finance
Abstract In a previous paper, a numerical method preserving positivity was constructed for stochastic age‐dependent population equations. However, only the local error of the balanced Euler method was verified. In this paper, we will give the global error of this numerical method in the mean square sense. Moreover, the strong convergence order is investigated which proves the convergence of the aforementioned method with strong order p = 1 2in the mean of global error. At last, we give some numerical experiments to illustrate the efficiency of our method.