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1st Edition - November 1, 2020
Authors: Snehashish Chakraverty, Nisha Rani Mahato
Computational Interval Methods for Engineering Applications explains how to use classical and advanced interval arithmetic to solve differential equations for a wide range of… Read more
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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.
1. Basics of interval analysis2. Classical interval arithmetic3. Interval linear differential equations4. Interval non-linear differential equations5. Parametric interval arithmetic6. Modal interval arithmetic7. Affine arithmetic8. Concepts of Contractors9. Differential inclusion10. Global optimisation using interval11. Interval uncertainty in linear structural problems12. Interval uncertainty in non-linear dynamic structural problems13. Interval uncertainty in control problems14. Interval uncertainty in system identification problems15. Interval uncertainty in other science and engineering problems
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