# Accurate stationary densities with partitioned numerical methods for stochastic differential equations

Burrage, Kevin and Lythe, Grant (2009) Accurate stationary densities with partitioned numerical methods for stochastic differential equations. Siam Journal on Numerical Analysis, 47 3: 1601-1618. doi:10.1137/060677148

Author Burrage, KevinLythe, Grant Accurate stationary densities with partitioned numerical methods for stochastic differential equations Siam Journal on Numerical Analysis   Check publisher's open access policy 0036-14291095-7170 2009-04 2009 Article (original research) 10.1137/060677148 47 3 1601 1618 18 Thomas A Manteuffel Philadelphia, Pa., USA SIAM Publications 2010 eng 0103 Numerical and Computational MathematicsC1010103 Category Theory, K Theory, Homological Algebra970101 Expanding Knowledge in the Mathematical Sciences We devise explicit partitioned numerical methods for second–order-in-time scalar stochastic differential equations, using one Gaussian random variable per timestep. The construction proceeds by analysis of the stationary density in the case of constant-coefficient linear equations, imposing exact stationary statistics in the position variable and absence of correlation between position and velocity; the remaining error is in the velocity variable. A new two-stage “reverse leapfrog” method has good properties in the position variable and is symplectic in the limit of zero damping. Explicit new “Runge–Kutta leapfrog” methods are constructed, sharing the property that $q_{n+1}=q_n+\frac{1}{2}(p_n+p_{n+1})\Delta t$, whose mean-square velocity order increases with the number of stages. ©2009 Society for Industrial and Applied Mathematics damped harmonic oscillators with noisestationary distributionstochastic Runge-Kutta methodsleapfrog methods C1 Confirmed Code

 Document type: Journal Article Article (original research) Excellence in Research Australia (ERA) - Collection 2010 Higher Education Research Data Collection Institute for Molecular Bioscience - Publications

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