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

儿童

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

CEDE

Eosinophils

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

confederacy

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.

证实

RODE-Taylor Schemes: General CaseRODE-Taylor schemes are presented for general RODEs with Hölder 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.

intolerance

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

progestogen

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

Infuriate

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