Abstract
Numerical stability of both explicit and implicit Runge-Kutta methods for solving ordinary differential equations with an additive noise term is studied. The concept of numerical stability of deterministic schemes is extended to the stochastic case, and a stochastic analogue of Dahlquist'sA-stability is proposed. It is shown that the discretization of the drift term alone controls theA-stability of the whole scheme. The quantitative effect of implicitness uponA-stability is also investigated, and stability regions are given for a family of implicit Runge-Kutta methods with optimal order of convergence.
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This author was partially supported by the Italian Consiglio Nazionale delle Ricerche.
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Hernandez, D.B., Spigler, R. A-stability of Runge-Kutta methods for systems with additive noise. BIT 32, 620–633 (1992). https://doi.org/10.1007/BF01994846
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DOI: https://doi.org/10.1007/BF01994846