Numerical Methods for Stochastic Partial Differential Equations with White Noise

• Main Authors: Zhang, Zhongqiang (Author), Karniadakis, George Em (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2017.
• Series: Applied Mathematical Sciences, 196
• Subjects: Mathematics.; Partial differential equations.; Numerical analysis.; Probabilities.; Numerical Analysis.; Probability Theory and Stochastic Processes.; Partial Differential Equations.

This book covers numerical methods for stochastic partial differential equations with white noise using the framework of Wong-Zakai approximation. The book begins with some motivational and background material in the introductory chapters and is divided into three parts. Part I covers numerical stoc...

Table of Contents:

• 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.