Abstract
Some generalized Newton multi-step iterative methods GMN(p,m) for solving a system of nonlinear equations are constructed. Generalized Newton multi-step iterative methods depend on parameters and consist of two parts, namely the base method and the multi-step part. In the base method we evaluate the Jacobian at the initial guess and then freeze it to solve system of linear equations in the multi-step part. Direct inversion of the Jacobian is an expansion operation and hence we utilize LU-factorization of the frozen Jacobian for moderately large system of linear equations. In the multi-step part we only solve lower and upper triangular systems that makes the computational process economical. The GMN(p,m )involve parameters and we are interested to find the parameters for maximizing the convergence order of iterative method. In the present article we explore some iterative method with p = 5 and convergence of order six for the base method. Each multi-step part adds one in the convergence order of the base method and hence the convergence order of GMN(5,m) (in this article) is 6 + m. The validity and numerical accuracy of the solution of the system of nonlinear equations are presented via numerical simulations.