Influence of the center condition on the two-step secant method (Q1798607)

The authors propose a two-step secant method in approximating a locally unique solution of a nonlinear equation in Banach spaces. The semi-local convergence analysis under weaker convergence conditions is proved. Local convergence analysis is established using only center-Lipschitz continuity conditions on divided differences. Numerical examples in gas dynamics and integral equations are presented to validate the theoretical results.