Siam j numer anal

Mean-square and asymptotic stability of numerical methods for stochastic ordinary differential equations. T1 - Mean-square and asymptotic stability of numerical methods for stochastic ordinary differential equations. N2 - Stability analysis of numerical methods for ordinary differential equations ODEs is motivated by the question 'for what choices of stepsize does the numerical method reproduce the characteristics of the test equation? In particular, we show that an extension of the deterministic A-stability property holds. We also plot mean-square stability regions for the case where the test equation has real parameters.

Milstein, M. Langevin type equations are an important and fairly large class of systems close to Hamiltonian ones. The methods derived are based on symplectic schemes for stochastic Hamiltonian systems. Special attention is paid to Hamiltonian systems with separable Hamiltonians and with additive noise.

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In this work, we propose a general framework for the construction of pressure law for phase transition. These equations of state are particularly suitable for a use in a relaxation finite volume scheme. The approach is based on a constrained convex optimization problem on the mixture entropy. It is valid for both miscible and immiscible mixtures. We also propose a rough pressure law for modelling a super-critical fluid.