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In this paper, we develop the partially truncated Euler–Maruyama method of a class of stochastic Volterra integro-differential equations with non-globally Lipschitz continuous coefficients. The mean-square exponential stability and the mean-square stability of the analytic solution and the partially truncated Euler–Maruyama method are investigated. Moreover, the theoretical results are illustrated by some numerical examples.

international journal of computer mathematics

Stability of the analytic solution and the partially truncated Euler–Maruyama method for a class of stochastic Volterra integro-differential equations with non-globally Lipschitz continuous coefficients