Non-iterative Transformation Methods Equivalence

Fazio, Riccardo

doi:10.1007/978-94-011-2050-0_21

Cited by 4 publications

(2 citation statements)

References 15 publications

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“…As far as the numerical solution of BVPs is concerned, we report here the definition within scaling invariance theory of an initial value method, referred in the literature also as a non-iterative TM [33]. To this end we consider the class of two-point BVPs…”

Section: Scaling Invariancementioning

confidence: 99%

On the equivalence of non-iterative transformation methods based on scaling and spiral groups

Fazio

Iacono

2009

Math. Meth. Appl. Sci.

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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.

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Section: Scaling Invariancementioning

confidence: 99%

On the equivalence of non-iterative transformation methods based on scaling and spiral groups

Fazio

Iacono

2009

Math. Meth. Appl. Sci.

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“…A different way to extend noniterative methods, namely, by defining a transformation of variables linking two different groups of transformations, was proposed in 1990 by Fazio [23,24]. Moreover, in the same way it is possible to prove that the utilization of stretching or of spiral group is equivalent (see [31] for details). Finally, an iterative extension applicable to general classes of problems has been recently developed by Fazio [27,30,33,34].…”

Section: Free or Movingmentioning

confidence: 99%

A Similarity Approach to the Numerical Solution of Free Boundary Problems

Fazio¹

1998

SIAM Rev.

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The aim of this work is to point out that within a similarity approach some classes of free boundary value problems governed by ordinary differential equations can be transformed to initial value problems. The interest in the numerical solution of free boundary problems arises because these are always nonlinear problems. Furthermore we show that free boundary problems arise also via a similarity analysis of moving boundary hyperbolic problems and they can be obtained as approximations of boundary value problems defined on infinite intervals. Most of the theoretical content of this survey is original: it generalizes and unifies results already available in literature. As far as applications of the proposed approach are concerned, three problems of interest are considered and numerical results for each of them are reported.

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Fazio

1999

Acta Applicandae Mathematicae

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Non-iterative Transformation Methods Equivalence

Cited by 4 publications

References 15 publications

On the equivalence of non-iterative transformation methods based on scaling and spiral groups

On the equivalence of non-iterative transformation methods based on scaling and spiral groups

A Similarity Approach to the Numerical Solution of Free Boundary Problems

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