This book provides a seamless approach to numerical algorithms, modern programming techniques and parallel computing. These concepts and tools are usually taught serially across different courses and different textbooks, thus observing the connection between them. The necessity of integrating these subjects usually comes after such courses are concluded (e.g., during a first job or a thesis project), thus forcing the student to synthesize what is perceived to be three independent subfields into one in order to produce a solution. The book includes both basic and advanced topics and places...
This book provides a seamless approach to numerical algorithms, modern programming techniques and parallel computing. These concepts and tools are usu...
In this book the Wong-Zakai approximation and Wiener chaos expansion are used for stochastic partial differential equations. In this framework, the reader is led to systems of deterministic partial differential equations with unknowns being the Wiener chaos expansion coefficients. The importance of the special structure of linear systems is emphasized. Sparse grid collocation methods are also discussed as well as generalized polynomial chaos. The advantages of the Wong-Zakai approximation are presented for stochastic ordinary and partial differential equations. Moreover, the Wick-Malliavin...
In this book the Wong-Zakai approximation and Wiener chaos expansion are used for stochastic partial differential equations. In this framework, the...
