Numerical methods for second-order stochastic differential equations
Data(s) |
2007
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Resumo |
We seek numerical methods for second‐order stochastic differential equations that reproduce the stationary density accurately for all values of damping. A complete analysis is possible for scalar linear second‐order equations (damped harmonic oscillators with additive noise), where the statistics are Gaussian and can be calculated exactly in the continuous‐time and discrete‐time cases. A matrix equation is given for the stationary variances and correlation for methods using one Gaussian random variable per timestep. The only Runge–Kutta method with a nonsingular tableau matrix that gives the exact steady state density for all values of damping is the implicit midpoint rule. Numerical experiments, comparing the implicit midpoint rule with Heun and leapfrog methods on nonlinear equations with additive or multiplicative noise, produce behavior similar to the linear case. |
Identificador | |
Publicador |
Society for Industrial and Applied Mathematics |
Relação |
DOI:10.1137/050646032 Burrage, Kevin, Lenane, Ian, & Lythe, Grant (2007) Numerical methods for second-order stochastic differential equations. SIAM Journal on Scientific Computing, 29(1), pp. 245-264. |
Fonte |
Faculty of Science and Technology |
Palavras-Chave | #010200 APPLIED MATHEMATICS #010300 NUMERICAL AND COMPUTATIONAL MATHEMATICS #080200 COMPUTATION THEORY AND MATHEMATICS #damped harmonic oscillators with noise, stationary distribution, stochastic Runge¿Kutta methods, implicit midpoint rule, multiplicative noise |
Tipo |
Journal Article |