Invariant Measures for Stochastic Nonlinear Schrödinger Equations [electronic resource] : Numerical Approximations and Symplectic Structures / by Jialin Hong, Xu Wang.

By: Hong, Jialin [author.]Contributor(s): Wang, Xu [author.] | SpringerLink (Online service)Material type: Text

TextSeries: Lecture Notes in Mathematics ; 2251Publisher: Singapore : Springer Singapore : Imprint: Springer, 2019Edition: 1st ed. 2019Description: XIV, 220 p. 14 illus., 13 illus. in color. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9789813290693Subject(s): Probabilities | Numerical analysis | Dynamics | Ergodic theory | Partial differential equations | Probability Theory and Stochastic Processes | Numerical Analysis | Dynamical Systems and Ergodic Theory | Partial Differential EquationsAdditional physical formats: Printed edition:: No title; Printed edition:: No titleDDC classification: 519.2 LOC classification: QA273.A1-274.9QA274-274.9Online resources: Click here to access online

Contents:

Invariant measures and ergodicity -- Invariant measures for stochastic differential equations -- Invariant measures for stochastic nonlinear Schrödinger equations -- Geometric structures and numerical schemes for nonlinear Schrödinger equations -- Numerical invariant measures for damped stochastic nonlinear Schrödinger equations -- Approximation of ergodic limit for conservative stochastic nonlinear Schrödinger equations.

In: Springer eBooksSummary: This book provides some recent advance in the study of stochastic nonlinear Schrödinger equations and their numerical approximations, including the well-posedness, ergodicity, symplecticity and multi-symplecticity. It gives an accessible overview of the existence and uniqueness of invariant measures for stochastic differential equations, introduces geometric structures including symplecticity and (conformal) multi-symplecticity for nonlinear Schrödinger equations and their numerical approximations, and studies the properties and convergence errors of numerical methods for stochastic nonlinear Schrödinger equations. This book will appeal to researchers who are interested in numerical analysis, stochastic analysis, ergodic theory, partial differential equation theory, etc.

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This book provides some recent advance in the study of stochastic nonlinear Schrödinger equations and their numerical approximations, including the well-posedness, ergodicity, symplecticity and multi-symplecticity. It gives an accessible overview of the existence and uniqueness of invariant measures for stochastic differential equations, introduces geometric structures including symplecticity and (conformal) multi-symplecticity for nonlinear Schrödinger equations and their numerical approximations, and studies the properties and convergence errors of numerical methods for stochastic nonlinear Schrödinger equations. This book will appeal to researchers who are interested in numerical analysis, stochastic analysis, ergodic theory, partial differential equation theory, etc.