Numerical Methods for Stochastic Partial Differential Equations with White Noise

Häftad, Engelska, 2018

Av Zhongqiang Zhang, George Em Karniadakis

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This book covers numerical methods for stochastic partial differential equations with white noise using the framework of Wong-Zakai approximation. In addition, stochastic Euler equations are exploited as an application of stochastic collocation methods, where a numerical comparison with other integration methods in random space is made.

Produktinformation

Utgivningsdatum2018-08-10
Mått155 x 235 x 27 mm
Vikt616 g
FormatHäftad
SpråkEngelska
SerieApplied Mathematical Sciences
Antal sidor394
FörlagSpringer International Publishing AG
ISBN9783319861814

Tillhör följande kategorier

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.

“Zhang and Karniadakis’ book may be used as a textbook, but it may also be considered as a reference for the state of the art concerning the numerical solution of stochastic differential equations involving white noise/Wiener processes/ Brownian motion. … Bibliographic notes address the state of the art in the field. Appendices give the necessary background in probability, stochastic calculus, semi-analytical approximation methods for stochastics differential equation, Gauss quadrature … . “ (José Eduardo Souze de Cursi, Mathematical Reviews, September, 2018)“It is an interesting book on numerical methods for stochastic partial differential equations with white noise through the framework of Wong-Zakai approximation. ... . It is to be noted that the authors provide a thorough review of topics both theoretical and computational exercises to justify the effectiveness of the developed methods. Further, the MATLAB files are made available to the researchers and readers to understand the state of art of numerical methods for stochastic partial differential equations.” (Prabhat Kumar Mahanti, zbMATH 1380.65021, 2018)