Titlebook: Random Ordinary Differential Equations and Their Numerical Solution; Xiaoying Han,Peter E. Kloeden Book 2017 Springer Nature Singapore Pte

兒童

Taylor Expansions for RODEs with Affine NoiseTaylor expansions are derived for RODEs with affine noise and general Affine-RODE-Taylor approximations are formulated.

CEDE

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Numerical Methods for Ordinary and Stochastic Differential EquationsOne-step numerical schemes for ODEs and It? SODEs are recalled.

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安慰

Numerical Schemes for RODEs with Affine NoiseOne-step numerical schemes for RODEs with affine noise are derived. Affine-RODE Taylor schemes for bounded, additive and commutative noise are considered. Derivative-free schemes are presented along with multi-step and Runge-Kutta schemes.

證實

RODE-Taylor Schemes: General CaseRODE-Taylor schemes are presented for general RODEs with H?lder continuous noise, and in particular essential RODE-Taylor schemes are considered. These schemes are also applied to RODEs with affine noise and compared with the heuristically derived schemes presented in the first chapter.

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Numerical StabilityThe numerical stability of implicit averaged and implicit multi-step schemes for nonlinear RODEs is determined.

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Stochastic Integrals: Simulation and ApproximationMethods for the simulations and approximation of stochastic integrals are given for Wiener processes, Ornstein-Uhlenbeck processes, fractional Brownian motions and Poisson processes. A method for calculating a finer approximation of the same sample path of a Winer process based on the Lévy construction is presented.

表皮

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Xiaoying Han,Peter E. KloedenMakes recent results on the derivation of higher order numerical schemes for random ordinary differential equations (RODEs) available to a broader readership.Develops numerical methods for random ODEs