Convergence of an iterative method for solving a class of nonlinear equations

In this paper, we consider the semilocal convergence of one popular iterative method for solving the nonlinear equations arising from the discretization of two-phase flow in porous media. This method is very important in petroleum reservoir engineering. The semilocal convergence of the method is proved under the proper assumptions coinciding with physical properties, which can provide the theoretical foundation for its applications. Numerical results of two-phase flow are also given.