Constructing an effcient multi{step iterative scheme for nonlinear system of equations

The objective of this research is to propose a new multi-step method in tackling a system of nonlinear equations. The constructed iterative scheme achieves a higher rate of convergence whereas only one LU decomposition per cycle is required to proceed. This makes the effciency index to be high as well in contrast to the existing solvers. The usefulness of the presented approach for tackling differential equations of nonlinear type with partial derivatives is also given.