Abstract
Here, we present a generalization of the classical Newton-Kantorovich method, which is frequently
used to approximate a solution to a nonlinear equation in a Banach space. The methods we suggest
are an improvement on the iterative Newton method. These new schemes are derived from the
integral formula given in Argyros (2007) (p. 33), Kelley (1995) (p. 65), and the classical numerical
schemes for function integration. Through several examples, we show how the experimental order of
convergence of the new methods is cubic. These schemes are used to find the numerical solution of
a nonlinear equation in one and two dimensions.
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