Numerical Methods for Stochastic Partial Differential Equations with White Noise -

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Auteur(s) : Collectif

Editeur : Springer International Publishing

Langue : Anglais

Parution : 31/08/2017

Format : Moyen, de 350g à 1kg

Expédition : 781

Dimensions : 24.1 x 16.0 x 2.8

ISBN : 3319575104

Résumé :

Includes both theoretical and computational exercises, allowing for use with mixed-level classes

Provides Matlab codes for examples

The first book to emphasizes the Wong-Zakai approximation

Offers an approach to stochastic modeling other than the common Monte Carlo methods

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Sommaire:
Preface.- Prologue.- Brownian Motion and Stochastic Calculus.- Numerical Methods for Stochastic Differential Equations.- Part I Stochastic Ordinary Differential Equations.- Numerical Schemes for SDEs with Time Delay Using the Wong-Zakai Approximation.- Balanced Numerical Schemes for SDEs with non-Lipschitz Coefficients.- Part II Temporal White Noise.- Wiener Chaos Methods for Linear Stochastic Advection-Diffusion-Reaction Equations.- Stochastic Collocation Methods for Differential Equations with White Noise.- Comparison Between Wiener Chaos Methods and Stochastic Collocation Methods.- Application of Collocation Method to Stochastic Conservation Laws.- Part III Spatial White Noise.- Semilinear Elliptic Equations with Additive Noise.- Multiplicative White Noise: The Wick-Malliavin Approximation.- Epilogue.- Appendices.- A. Basics of Probability.- B. Semi-analytical Methods for SPDEs.- C. Gauss Quadrature.- D. Some Useful Inequalities and Lemmas.- E. Computation of Convergence Rate.