Tamed-Euler method for hybrid stochastic differential equations with Markovian switching

This paper develops a numerical scheme for approximating solutions of stochastic differential equations with Markovian switching under such conditions that allow drift coefficients being locally one-sided Lipschitz continuous, and diffusion coefficients being locally Lipschitz continuous. The strong convergence of the algorithm is proved. In addition, under the assumption of polynomial growth rate of drift and global Lipschitz continuity, the classical rate of convergence is also obtained. Some numerical examples are provided for demonstration purpose.