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A new stepsize change technique for Adams methods

M. Calvo

M. Calvo

IUMA-Dpto. Matemática AplicadaZaragoza, Spain
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Calvo, M.
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J.I. Montijano

J.I. Montijano

IUMA-Dpto. Matemática AplicadaZaragoza, Spain
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Montijano, J.I.
 and 
L. Rández

L. Rández

IUMA-Dpto. Matemática AplicadaZaragoza, Spain
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Rández, L.
  
Nov 18, 2016
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Published Online: Nov 18, 2016
Page range: 547 - 558
Received: Nov 07, 2016
Accepted: Nov 18, 2016
DOI: https://doi.org/10.21042/AMNS.2016.2.00043
Keywords
© 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

Plot of the φ1(α)) for AM2 methods for T1 and T3 techniques
Plot of the φ1(α)) for AM2 methods for T1 and T3 techniques

Fig. 2

Spectral radius of the AM2 methods for T1, T3 and interpolation techniques
Spectral radius of the AM2 methods for T1, T3 and interpolation techniques

Fig. 3

Spectral radius of the AM3 methods for T1, T3 and interpolation techniques
Spectral radius of the AM3 methods for T1, T3 and interpolation techniques

Fig. 4

Spectral radius of the AM4 methods for T1, T3 and interpolation techniques
Spectral radius of the AM4 methods for T1, T3 and interpolation techniques

Fig. 5

Spectral radius of the AM5 methods for T1, T3 and interpolation techniques
Spectral radius of the AM5 methods for T1, T3 and interpolation techniques

Fig. 6

Spectral radius of the AM6 methods for T1, T3 and interpolation techniques
Spectral radius of the AM6 methods for T1, T3 and interpolation techniques

Fig. 7

Spectral radius of the AM7 methods for T1, T3 and interpolation techniques. Note that there exists an interval near 0.8 where the spectral radius of T1 and interpolation techniques is greater than one.
Spectral radius of the AM7 methods for T1, T3 and interpolation techniques. Note that there exists an interval near 0.8 where the spectral radius of T1 and interpolation techniques is greater than one.

T1

T3

interp.

k

rk

Mk(rk)

αk

rk

Mk(rk)

αk

rk

Mk(rk)

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]

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