Wang, Lasheng; Wang, Xiaojie Convergence of the semi-implicit Euler method for stochastic age-dependent population equations with Poisson jumps. (English) Zbl 1193.60089 Appl. Math. Modelling 34, No. 8, 2034-2043 (2010). Summary: We consider semi-implicit methods for stochastic age-dependent population equations with Poisson jumps. The main purpose of this paper is to show the convergence of the numerical approximation solution to the true solution with strong order \(p=\frac12\). Cited in 1 ReviewCited in 17 Documents MSC: 60H35 Computational methods for stochastic equations (aspects of stochastic analysis) 65C30 Numerical solutions to stochastic differential and integral equations Keywords:stochastic age-dependent population equations; semi-implicit Euler method; strong convergence; Poisson jumps PDFBibTeX XMLCite \textit{L. Wang} and \textit{X. Wang}, Appl. Math. Modelling 34, No. 8, 2034--2043 (2010; Zbl 1193.60089) Full Text: DOI References: [1] Cushing, J. M., The dynamics of hierarchical age-structured populations, J. Math. Biol., 32, 705-729 (1994) · Zbl 0823.92018 [2] Allen, L. J.S.; Thrasher, D. B., The effects of vaccination in an age-dependent model for varicella and herpes zoster, IEEE Trans. Automat. Control., 43, 779-789 (1998) [3] Zhang, Q.; Liu, W.; Nie, Z., Existence, uniqueness and exponential stability for stochastic age-dependent population, Appl. Math. Comput., 154, 183-201 (2004) · Zbl 1051.92033 [4] Pang, W.; Li, R.; Min, Liu, Convergence of the semi-implicit Euler method for stochastic age-dependent population equations, Appl. Math. Comput., 195, 466-474 (2008) · Zbl 1159.65010 [5] Li, R.; Pang, W.; Wang, Q., Numerical analysis for stochastic age-dependent population equations with Poisson jumps, J. Math. Anal. Appl., 327, 1214-1224 (2007) · Zbl 1115.65008 [6] Gardon, Albert, The order of approximatons for solutions of ito-type stochastic differential equations with jumps, Stoch. Anal. Appl., 22, 679-699 (2004) · Zbl 1056.60065 [7] Fima, A.; Klebaner, C., Introduction to Stochastic Calculus with Applications (1998), Imperial College Press.: Imperial College Press. London · Zbl 0926.60002 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.