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In this paper numerical methods for solving stochastic differential equationswith Markovian switching (SDEwMSs) are developed by pathwise approximation. Theproposed family of strong predictor-corrector Euler-Maruyama methods isdesigned to overcome the propagation of errors during the simulation of anapproximate path. This paper not only shows the strong convergence of thenumerical solution to the exact solution but also reveals the order of theerror under some conditions on the coefficient functions. A natural analogue of$p$-stability criterion is studied. Numerical examples are given to illustratethe computational efficiency of the new predictor-corrector Euler-Maruyamaapproximation.

Strong Predictor-Corrector Euler-Maruyama Methods for Stochastic Differential Equations with Markovian Switching