Perturbed iterative solution of coupled nonlinear systems with application to fluid dynamics

The perturbed iterative scheme developed in [3] is extended in this work to solve coupled systems of nonlinear equations. The algorithm consists of computing distinct perturbation parameters for each system at each iteration and adding these to corresponding nonlinear Gauss-Seidel iterates. It has been found computationally that such an algorithm significantly improves the convergence properties of Gauss-Seidel iterations. The method has been successfully applied to several coupled nonlinear systems of equations some of which are discussed in this work.