This paper presents a pathwisely jump-adapted approximation of the Poisson driven Markov processes governed by stochastic differential equations.Any trajectory of the processes is divided into continuous phases. Within each phase, the corresponding ODEs are established and solved by the Runge Kutta schemes.The method is applied to investigate the Langevin equation as well as the Duffing-Van der Poloscillator.

The paper gives a necessary condition of asymptotic mean square stability for the implicit Milstein scheme for linear complex-valued stochastic jump-diffusion equations and shows how the stability depends on the implicitness of the scheme.

In this paper, the well-testing analysis is made, based on the finite element method, for a naturally fractured reservoir with two intersection boundaries. Covergence of the numerical solution is proved and some typical theoretical curves of the pressure are presented in the cases of different location of the well position, different types of boundary conditions, and different intersection angles of the boundaries.