An R-order four iteration in Banach space
In this paper, we apply a R-order four iterative method to solve non-linear operator equations in Banach spaces. We prove a semilocal convergence theorem which guarantees local convergence with R-order four under conditions similar to those of the Newton-Kantorovich theorem, assuming that the second derivative is bounded, and also give a priori error bounds. Moreover, we apply our results to the numerical solution of a non-linear boundary value problem of second-order.
convergence a priori error bounds boundary value problems recurrence relations