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
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
Snehashish Chakraverty is a recipient of various awards viz. the Indian Science Congress Association's Platinum Jubilee Lecture Award, CSIR Young Scientist, BOYSCAST, INSA International Bilateral Exchange awards etc. and the Editor-in-Chief of the International Journal of Fuzzy Computation and Modelling. His research focuses on the application of numerical modelling to a broad range of problems, and he has been widely published in both books and peer-reviewed journals.
Mahato, Nisha Rani
NR Mahato's research focuses on structural dynamics, interval analysis, and eigenvalue problems.