Computational Interval Methods for Engineering Applications explains how to use classical and advanced interval arithmetic to solve differential equations for a wide range of scientific and engineering problems. In mathematical models where there are variables and parameters of uncertain value, interval methods can be used as an efficient tool for handling this uncertainty. In addition, it can produce rigorous enclosures of solutions of practical problems governed by mathematical equations. Other topics discussed in the book include linear differential equations in areas such as robotics, control theory, and structural dynamics, and in nonlinear oscillators, such as Duffing and Van der Pol.
The chaotic behavior of the enclosure of oscillators is also covered, as are static and dynamic analysis of engineering problems using the interval system of linear equations and eigenvalue problems, thus making this a comprehensive resource.
- Explains how interval arithmetic can be used to solve problems in a range of engineering disciplines, including structural and control
- Gives unique, comprehensive coverage of traditional and innovative interval techniques, with examples addressing both linear and nonlinear differential equations
- Provides full mathematical details of the governing differential equations used to solve a wide range of problems
Table of Contents
1. Basics of interval analysis 2. Classical interval arithmetic 3. Interval linear differential equations 4. Interval non-linear differential equations 5. Parametric interval arithmetic 6. Modal interval arithmetic 7. Affine arithmetic 8. Concepts of Contractors 9. Differential inclusion 10. Global optimisation using interval 11. Interval uncertainty in linear structural problems 12. Interval uncertainty in non-linear dynamic structural problems 13. Interval uncertainty in control problems 14. Interval uncertainty in system identification problems 15. Interval uncertainty in other science and engineering problems
Authors
Chakraverty, Snehashish Dr. Snehashish Chakraverty has 29 years of experience as a researcher and teacher. Presently he is working in the Department of Mathematics (Applied Mathematics Group), at the National Institute of Technology Rourkela, Odisha, India as a Full Professor. Prior to this he was with CSIR-Central Building Research Institute, Roorkee, India. He has a Ph.D. from IIT Roorkee in Computer Science. Thereafter he did his post-doctoral research at Institute of Sound and Vibration Research (ISVR), University ofSouthampton, U.K. and at the Faculty of Engineering and Computer Science, Concordia University, Canada. He was also a visiting professor at Concordia and McGill universities, Canada, and visiting professor at the University of Johannesburg, South Africa. He has authored/co-authored 14 books, published 315 research papers in journals and conferences, and has four more books in development. Dr. Chakraverty is on the Editorial Boards of various International Journals, Book Series and Conferences. Prof. Chakraverty is the Chief Editor of the International Journal of Fuzzy Computation and Modelling (IJFCM), Associate Editor of Computational Methods in Structural Engineering, Frontiers in Built Environment, and is the Guest Editor for several other journals. He was the President of the Section of Mathematical sciences (including Statistics) of the Indian Science Congress. Prof. Chakraverty has undertaken around 16 research projects as Principle Investigator funded by international and national agencies. His present research area includes Differential Equations (Ordinary, Partial and Fractional), Soft Computing and Machine Intelligence (Artificial Neural Network, Fuzzy and Interval Computations), Numerical Analysis, Mathematical Modeling, Uncertainty Modelling, Vibration and Inverse Vibration Problems. Mahato, Nisha Rani NR Mahato's research focuses on structural dynamics, interval analysis, and eigenvalue problems.
