A variable local relaxation technique in nonlinear problems

Application of under and over-relaxation is a very useful technique in solution of nonlinear problems. However, the choice of the relaxation factor is problem dependent and difficult to estimate. In this work we propose a new method in which the relaxation factor is chosen automatically by the computer code, based on the dynamics of the convergence process. In addition, the local application of relaxation factors is introduced, so that different unknowns have different relaxation factors. Two examples are presented to demonstrate the proposed method´s efficiency