# Seventh Convergence Order Solvers Free Of Derivatives For Solving Equations In Banach Space

## Seventh convergence order solvers free of derivatives

### Abstract

We study a seventh convergence order solver introduced earlier on the j−dimensional Euclidean space for solving systems of equations. We use hypotheses only on the divided differences of order one in contrast to the earlier study using hypotheses on derivatives reaching up to order eight although these derivatives do not appear on the solver. This way we expand the applicability of the solver, and in the more general setting of Banach space valued operators. Numerical examples complement the theoretical results.

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