A new class of interval methods with higher order of convergence

In this paper we introduce a new class of interval methods for enclosing a simple root of a nonlinear equation. For each nonnegative integerp we describe an iterative procedure belonging to this class which requiresp+1 function values and an interval evaluation of the second derivative per step. The order of convergence of the iterative procedure grows exponentially withp. Forp≥4 this order is strictly greater than (left( {frac{{1 + sqrt 5 }}{2}} right)^{p + 2} ) .