Random differential equations in scientific computing / / Tobias Neckel, Florian Rupp.

• Superior document: Versita Discipline: Mathematics
• VerfasserIn: Neckel, Tobias,; Rupp, Florian,
• TeilnehmendeR: Rupp, Florian,
• Place / Publishing House: London, England : : Versita, Versita Limited,, 2013.; ©2013
• Year of Publication: 2013
• Language: English
• Series: Versita discipline. Mathematics.
• Physical Description: 1 online resource (650 pages) :; illustrations.
• Notes: Bibliographic Level Mode of Issuance: Monograph

This book is a holistic and self-contained treatment of the analysis and numerics of random differential equations from a problem-centred point of view. An interdisciplinary approach is applied by considering state-of-the-art concepts of both dynamical systems and scientific computing. The red line pervading this book is the two-fold reduction of a random partial differential equation disturbed by some external force as present in many important applications in science and engineering. First, the random partial differential equation is reduced to a set of random ordinary differential equations in the spirit of the method of lines. These are then further reduced to a family of (deterministic) ordinary differential equations. The monograph will be of benefit, not only to mathematicians, but can also be used for interdisciplinary courses in informatics and engineering.

Table of Contents

Front matter -- Preface -- Acknowledgments -- Contents -- Part I Motivation and Decomposition of Multi-Storey Building Excitation Problems -- Part II The Path-Wise Deterministic Setting -- Part III Efficient Data Structures & the Propagation of Random Excitations -- Part IV Path-Wise Solutions of Random Differential Equations and Their Simulation -- Part V The Workshop Project -- Index -- Bibliography