Abstract
The non-iterative numerical solution of nonlinear boundary value problems is a subject of great interest. The present note is concerned with the theory of non-iterative transformation methods. These methods are defined within group invariance theory. Here we prove the equivalence between the two non-iterative transformation methods defined by the stretching group and the spiral group respectively. Then we point out the prominent role of stretching transformations in solving non-iteratively boundary value problems governed by ordinary differential equations.
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