Convergence of the split-step θ-method for stochastic age-dependent population equations with Poisson jumps

In this paper, a new split-step θ (SSθ) method for stochastic age-dependent population equations with Poisson jumps is constructed. The main aim of this paper is to investigate the convergence of the SSθ method for stochastic age-dependent population equations with Poisson jumps. It is proved that the proposed method is convergent with strong order 1/2 under given conditions. Finally, an example is simulated to verify the results obtained from theory, the results show that the SSθ method has better accuracy compared to the Euler method.