Date of Online Publication: 02/11/2010
Keywords: Stochastic Differential Equations, Additive Noise, Numerical Solution, Runge–
Kutta methods
Periodic orbits, Numerical drift.
Authors: Foivos Xanthos and George Papageorgiou

Abstract: In this paper we study the numerical treatment of Stochastic Differential Equations
with additive noise and one dimensional Wiener process. We develop two, three and
four stage Runge–Kutta methods which attain deterministic order up to four and stochastic
order up to one and a half specially constructed for this class of problems. Numerical tests
and comparisons with other known methods in the solution of various problems justify our
effort, especially for our three stages methods.

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