A new convergence and positivity analysis of balanced Euler method for stochastic age‐dependent population equations. Issue 2 (30th October 2020)

• Record Type: Journal Article
• Authors: Tan, Jianguo; Mayavel, Pichamuthu; Rathinasamy, Anandaraman; Cao, Honglei
• Is Part Of: Numerical methods for partial differential equations. Volume 37:Issue 2(2021)
• Page Start: 1752
• Page End: 1765
• Publication Date: 2020-10-30
• Subjects: balanced methods -- convergence -- numerical solutions -- stochastic age‐dependent population equations; Differential equations, Partial -- Numerical solutions -- Periodicals; 515.353
• DOI: 10.1002/num.22606
• Languages: English
• ISSNs: 0749-159X

Abstract

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 2 in the mean of global error. At last, we give some numerical experiments to illustrate the efficiency of our method.