Asymptotic mean-square boundedness of the numerical solutions of stochastic age-dependent population equations with Poisson jumps. (English) Zbl 1426.92061
Summary: This paper focuses on asymptotic mean-square boundedness of several numerical methods applied to a class of stochastic age-dependent population equations with Poisson jumps. The conditions under which the underlying systems are asymptotic mean-square boundedness are considered. It is shown that the asymptotic mean-square boundedness is preserved by the compensated split-step backward Euler method and compensated backward Euler method without any restriction on stepsize, while the split-step backward Euler method and backward Euler method could reproduce asymptotic mean-square boundedness under a stepsize constraint. The results indicate that compensated numerical methods achieve superiority over non-compensated numerical methods in terms of asymptotic mean-square boundedness. Finally, an example is given for illustration.
MSC:
| 92D25 | Population dynamics (general) |
Keywords:
asymptotic mean-square boundedness; compensated numerical methods; non-compensated numerical methods; stochastic age-dependent population equations; Poisson jumpsReferences:
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