A ( α )-Stable Linear Multistep Methods for Stiff IVPs in ODEs

R. I. Okuonghae; M. N. O. Ikhile

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2011)

  • Volume: 50, Issue: 1, page 73-90
  • ISSN: 0231-9721

Abstract

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In this paper, a class of A( α )-stable linear multistep formulas for stiff initial value problems (IVPs) in ordinary differential equations (ODEs) is developed. The boundary locus of the methods shows that the schemes are A-stable for step number k ≤ 3 and stiffly stable for k = 4 , 5 and 6 . Some numerical results are reported to illustrate the method.

How to cite

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Okuonghae, R. I., and Ikhile, M. N. O.. "A ($\alpha $)-Stable Linear Multistep Methods for Stiff IVPs in ODEs." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 50.1 (2011): 73-90. <http://eudml.org/doc/197074>.

@article{Okuonghae2011,
abstract = {In this paper, a class of A($\alpha $)-stable linear multistep formulas for stiff initial value problems (IVPs) in ordinary differential equations (ODEs) is developed. The boundary locus of the methods shows that the schemes are A-stable for step number $k\le 3$ and stiffly stable for $k=4, 5$ and $6$. Some numerical results are reported to illustrate the method.},
author = {Okuonghae, R. I., Ikhile, M. N. O.},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {second derivative method; collocation and interpolation; initial value problem; stiff stability; boundary locus; second derivative method; collocation and interpolation; initial value problem; stiff stability; boundary locus; stiff initial value problems},
language = {eng},
number = {1},
pages = {73-90},
publisher = {Palacký University Olomouc},
title = {A ($\alpha $)-Stable Linear Multistep Methods for Stiff IVPs in ODEs},
url = {http://eudml.org/doc/197074},
volume = {50},
year = {2011},
}

TY - JOUR
AU - Okuonghae, R. I.
AU - Ikhile, M. N. O.
TI - A ($\alpha $)-Stable Linear Multistep Methods for Stiff IVPs in ODEs
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2011
PB - Palacký University Olomouc
VL - 50
IS - 1
SP - 73
EP - 90
AB - In this paper, a class of A($\alpha $)-stable linear multistep formulas for stiff initial value problems (IVPs) in ordinary differential equations (ODEs) is developed. The boundary locus of the methods shows that the schemes are A-stable for step number $k\le 3$ and stiffly stable for $k=4, 5$ and $6$. Some numerical results are reported to illustrate the method.
LA - eng
KW - second derivative method; collocation and interpolation; initial value problem; stiff stability; boundary locus; second derivative method; collocation and interpolation; initial value problem; stiff stability; boundary locus; stiff initial value problems
UR - http://eudml.org/doc/197074
ER -

References

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