<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In this paper a new technique for stepsize changing in the numerical solution of Initial Value Problems for ODEs by means of Adams type methods is considered. The computational cost of the new technique is equivalent to those of the well known interpolation technique (IT). It is seen that the new technique has better stability properties than the IT and moreover, its leading error term is smaller. These facts imply that the new technique can outperform the IT.</p></abstract>

In this paper a new technique for stepsize changing in the numerical solution of Initial Value Problems for ODEs by means of Adams type methods is considered. The computational cost of the new technique is equivalent to those of the well known interpolation technique (IT). It is seen that the new technique has better stability properties than the IT and moreover, its leading error term is smaller. These facts imply that the new technique can outperform the IT.

A new stepsize change technique for Adams methods

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"A new stepsize change technique for Adams methods"}

In this paper a new technique for stepsize changing in the numerical solution of Initial Value Problems for ODEs by means of Adams type methods is considered....

	T1			T3			interp.

k	r_k	M_k(r_k)	α_k	r_k	M_k(r_k)	α_k	r_k	M_k(r_k)
2	1.803	[0, 1.803]	0.8122	1.803	[0, 1.803]	0.9184	1.695	[0, 1.695]
3	1.462	[0, 1.491]	0.8000	1.422	[0, 1.461]	0.9898	1.419	[0, 1.437]
4	1.315	[0, 1.321]	0.8000	1.296	[0, 1.321]	1.0020	1.297	[0, 1.297]
5	1.221	[0, 1.251]	0.9000	1.094	[0, 1.123]	0.9796	0.905	[0, 1.056]
6	1.120	[0, 1.172]	0.7489	1.017	[0, 1.096]	1.0351	1.170	[0, 0.257] ∪ [.971, 1.181]

A new stepsize change technique for Adams methods

Pubblicato online: 18 nov 2016

Pagine: 547 - 558

Ricevuto: 07 nov 2016

Accettato: 18 nov 2016

DOI: https://doi.org/10.21042/AMNS.2016.2.00043

Parole chiave
stepsize change, linear multistep methods

© 2016 M. Calvo, J.I. Montijano, L. Rández, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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A new stepsize change technique for Adams methods

Pubblicato online: 18 nov 2016

Pagine: 547 - 558

Ricevuto: 07 nov 2016

Accettato: 18 nov 2016

DOI: https://doi.org/10.21042/AMNS.2016.2.00043

Parole chiavestepsize change, linear multistep methods

© 2016 M. Calvo, J.I. Montijano, L. Rández, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Fig. 6

Fig. 7

Parole chiave
stepsize change, linear multistep methods