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 stochastic ordinary differential equations. Here the authors start with numerical methods for SDEs with delay using the Wong-Zakai approximation and finite difference in time. Part II covers temporal white noise. Here the authors consider SPDEs as PDEs driven by white noise, where discretization of white noise (Brownian motion) leads to PDEs with smooth noise, which can then be treated by numerical methods for PDEs. In this part, recursive algorithms based on Wiener chaos expansion and stochastic collocation methods are presented for linear stochastic advection-diffusion-reaction equations. 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. Part III covers spatial white noise. Here the authors discuss numerical methods for nonlinear elliptic equations as well as other equations with additive noise. Numerical methods for SPDEs with multiplicative noise are also discussed using the Wiener chaos expansion method. In addition, some SPDEs driven by non-Gaussian white noise are discussed and some model reduction methods (based on Wick-Malliavin calculus) are presented for generalized polynomial chaos expansion methods. Powerful techniques are provided for solving stochastic partial differential equations.
Numerical Methods for Stochastic Partial Differential Equations with White Noise PDF Free Download
November 1, 2022
You may also like
APPLIED MATHEMATICS
Boundary Value Problems, Integral Equations and Related Problems by Liang fook Lye PDF
October 10, 2023
In this volume, we report new results about various boundary value problems for partial differential equations and functional equations, theory and methods of...
APPLIED MATHEMATICS
Solution Manual Advanced Modern Engineering Mathematics, 4th Edition by Glyn James PDF
October 10, 2023
This market-leading text is known for its comprehensive coverage, careful and correct mathematics, outstanding exercises, and self contained subject matter...
APPLIED MATHEMATICS
Advanced Modern Engineering Mathematics, 4th Edition by Glyn James PDF
October 10, 2023
This market-leading text is known for its comprehensive coverage, careful and correct mathematics, outstanding exercises, and self contained subject matter...
Recent Posts
- Algebra 3 Homological Algebra and Its Applications by Ramji Lal PDF
- Heat Transfer Physics 2nd Edition By Massoud Kaviany PDF
- Lavin’s Radiography for Veterinary Technicians, 6th Edition by Marg Brown PDF
- Principles of Physics, 10th Edition by David Halliday PDF
- The Dog Behavior Problem Solver by Teoti Anderson PDF
Add Comment