Ball convergence analysis of Jarratt-type sixth-order method and its applications in solving some chemical problems

In this paper, with the aim of approximate the ball convergence of nonlinear equation, we study the local properties of a class of sixth-order Jarratt-type iterative methods in Banach spaces. By utilizing the first-order Fréchet derivative, we establish the local convergence. At last, the nonlinear equations related to the gas-state equation, the continuous stirred tank reactor (CSTR) and the problem of azeotropic point of a binary solutions are solved using this iterative method, and the applicability of the theoretical results is proved.