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.

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

FAZIO, Riccardo;IACONO, SALVATORE
2010-01-01

Abstract

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.
2010
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11570/1890457
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