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Solving Nonlinear Equations Using Interval Arithmetic

Y. Akyildiz
M. Bartholomew-Biggs
Journal / Anthology


The interval version of the bisection method is a powerful and relatively recently discovered way of finding several roots of a nonlinear equation. In this note we shall illustrate how a version of bisection method which uses interval arithmetic can find all the roots of an equation which lie within a given range. We implement this method in Mathematica by using the built-in function RealInterval and demonstrate it on some examples which cannot be easily handled by other built-in functions, such as Solve, NSolve, and FindRoot.

*Applied Mathematics > Numerical Methods