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We propose a new tamed Milstein-type scheme for stochastic differentialequation with Markovian switching when drift coefficient is assumed to growsuper-linearly. The strong rate of convergence is shown to be equal to $1.0$under mild regularity (e.g. once differentiability) requirements on drift anddiffusion coefficients. Novel techniques are developed to tackle two-folddifficulties arising due to jumps of the Markov chain and the reduction ofregularity requirements on the coefficients.

On Explicit Tamed Milstein-type scheme for Stochastic Differential Equation with Markovian Switching