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. Copyright © 2009 John Wiley & Sons, Ltd.