Introduction to Interval Analysis and Solving the Problems with Interval Uncertainties
Navid Razmjooy · 2023
Minkowski is a classical method that extends and generalizes operations such as addition, subtraction, multiplication, and even division to the interval set. In the proposed interval representation, the difference is based on the Min-kowski method. Addressing dynamical problems under interval uncertainties is more challenging compared to static problems. When applying interval methods to solve interval differential equations, the high iteration involved increases the likelihood of the wrapping effect, which may even lead to divergence in numerical methods. In this chapter, an improved method for solving differential equations with interval uncertainty is proposed. Therefore, initial value problem (IVP) differential equations are studied in the presence of interval uncertainties by using a generalized Hukuhara-based Runge-Kutta method (GIRKM) from both theory and practical points of view.