Recent Trends in Wave Mechanics and Vibrations pp 455-468 | Cite as

# Validated Enclosure of Uncertain Nonlinear Equations Using SIVIA Monte Carlo

## Abstract

The dynamical systems in various science and engineering problems are often governed by nonlinear equations (differential equations). Due to insufficiency and incompleteness of system information, the parameters in such equations may have uncertainty. Interval analysis serves as an efficient tool for handling uncertainties in terms of closed intervals. One of the major problems with interval analysis is handling “dependency problems” for computation of the tightest range of solution enclosure or exact enclosure. Such dependency problems are often observed while dealing with complex nonlinear equations. In this regard, initially, two test problems comprising interval nonlinear equations are considered. The Set Inversion via Interval Analysis (SIVIA) along with the Monte Carlo approach is used to compute the exact enclosure of the test problems. Further, the efficiency of the proposed approach has also been verified for solving nonlinear differential equation (Van der Pol oscillator) subject to interval initial conditions.

## Keywords

Uncertain nonlinear equations Nonlinear oscillator Dependency problem SIVIA Monte Carlo Contractor## References

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