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By Hernandez D. B., Spigler R.

Numerical balance of either specific and implicit Runge-Kutta equipment for fixing traditional differential equations with an additive noise time period is studied. the concept that of numerical balance of deterministic schemes is prolonged to the stochastic case, and a stochastic analogue of Dahlquist's A-stability is proposed. it really is proven that the discretization of the flow time period on my own controls the A-stability of the full scheme. The quantitative influence of implicitness upon A-stability can be investigated, and balance areas are given for a kin of implicit Runge-Kutta equipment with optimum order of convergence.

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A -stability of Runge-Kutta methods for systems with additive noise by Hernandez D. B., Spigler R.

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