On the Equivalence of Non-iterative Transformation Methods Based on Scaling and Spiral Groups

The non-iterative numerical solution of nonlinear boundary value problems is a subject of great interest. The present paper is concerned with the theory of non-iterative transformation methods (TMs). These methods are defined within group invariance theory. Here we prove the equivalence between two non-iterative TMs defined by the scaling group and the spiral group, respectively. Then, we report on numerical results concerning the steady state temperature space distribution in a non-linear heat generation model. These results improve the ones, available in the literature, obtained by using the invariance with respect to a spiral group.