Perturbed iterative solution of nonlinear equations with applications to fluid dynamics

In this work a technique has been developed to solve a set of nonlinear equations with the assumption that a solution exists. The algorithm involves nonlinear Gauss-Seidel iteractions and at each iteration the value of the iterate is added to a predetermined perturbation parameter which is computed in terms of quantities already known. This perturbation parameter has two properties: (i) it determines the mode of convergence, that means it shows how many more computations are required so that convergence may be achieved, and (ii) it accelerates the rate of convergence. The algorithm is computationally simple. Several nonlinear equations have been studied. The results seem to be encouraging.