Highly Stable Super-Implicit Hybrid Methods for Special Second Order IVPs

Oluwasegun Micheal Ibrahim; Monday Ndidi Oziegbe Ikhile

doi:doi:10.11648/j.ajasr.20170303.11

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Highly Stable Super-Implicit Hybrid Methods for Special Second Order IVPs

Oluwasegun Micheal Ibrahim, Monday Ndidi Oziegbe Ikhile

Published in American Journal of Applied Scientific Research (Volume 3, Issue 3)

Received: 29 June 2017 Accepted: 14 July 2017 Published: 31 October 2017

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Abstract

The idea of symmetric super-implicit linear multi-step methods (SSILMMs) necessitates the use of not just past and present solution values of the ordinary differential equations (ODEs), but also, future values of the solution. Such methods have been proposed recently for the numerical solution of second-order ODEs. One technique to obtain more accurate integration process is to construct linear multi-step methods with hybrid points employing future solution values. In this regard, we construct families of Stӧrmer-Cowell type hybrid SSILMMs having higher order than that of the symmetric super-implicit method recently proposed for the same step number using the Taylors series approach. The newly derived hybrid SSILMMs are p-stable with accurate results when tested on some special second order IVPs.

Published in	American Journal of Applied Scientific Research (Volume 3, Issue 3)
DOI	10.11648/j.ajasr.20170303.11
Page(s)	21-27
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Super-Implicit, Hybrid LMM, Stӧrmer-Cowell Method, P-stability

References

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APA Style

Oluwasegun Micheal Ibrahim, Monday Ndidi Oziegbe Ikhile. (2017). Highly Stable Super-Implicit Hybrid Methods for Special Second Order IVPs. American Journal of Applied Scientific Research, 3(3), 21-27. https://doi.org/10.11648/j.ajasr.20170303.11

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ACS Style

Oluwasegun Micheal Ibrahim; Monday Ndidi Oziegbe Ikhile. Highly Stable Super-Implicit Hybrid Methods for Special Second Order IVPs. Am. J. Appl. Sci. Res. 2017, 3(3), 21-27. doi: 10.11648/j.ajasr.20170303.11

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AMA Style

Oluwasegun Micheal Ibrahim, Monday Ndidi Oziegbe Ikhile. Highly Stable Super-Implicit Hybrid Methods for Special Second Order IVPs. Am J Appl Sci Res. 2017;3(3):21-27. doi: 10.11648/j.ajasr.20170303.11

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@article{10.11648/j.ajasr.20170303.11,
  author = {Oluwasegun Micheal Ibrahim and Monday Ndidi Oziegbe Ikhile},
  title = {Highly Stable Super-Implicit Hybrid Methods for Special Second Order IVPs},
  journal = {American Journal of Applied Scientific Research},
  volume = {3},
  number = {3},
  pages = {21-27},
  doi = {10.11648/j.ajasr.20170303.11},
  url = {https://doi.org/10.11648/j.ajasr.20170303.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajasr.20170303.11},
  abstract = {The idea of symmetric super-implicit linear multi-step methods (SSILMMs) necessitates the use of not just past and present solution values of the ordinary differential equations (ODEs), but also, future values of the solution. Such methods have been proposed recently for the numerical solution of second-order ODEs. One technique to obtain more accurate integration process is to construct linear multi-step methods with hybrid points employing future solution values. In this regard, we construct families of Stӧrmer-Cowell type hybrid SSILMMs having higher order than that of the symmetric super-implicit method recently proposed for the same step number using the Taylors series approach. The newly derived hybrid SSILMMs are p-stable with accurate results when tested on some special second order IVPs.},
 year = {2017}
}

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TY  - JOUR
T1  - Highly Stable Super-Implicit Hybrid Methods for Special Second Order IVPs
AU  - Oluwasegun Micheal Ibrahim
AU  - Monday Ndidi Oziegbe Ikhile
Y1  - 2017/10/31
PY  - 2017
N1  - https://doi.org/10.11648/j.ajasr.20170303.11
DO  - 10.11648/j.ajasr.20170303.11
T2  - American Journal of Applied Scientific Research
JF  - American Journal of Applied Scientific Research
JO  - American Journal of Applied Scientific Research
SP  - 21
EP  - 27
PB  - Science Publishing Group
SN  - 2471-9730
UR  - https://doi.org/10.11648/j.ajasr.20170303.11
AB  - The idea of symmetric super-implicit linear multi-step methods (SSILMMs) necessitates the use of not just past and present solution values of the ordinary differential equations (ODEs), but also, future values of the solution. Such methods have been proposed recently for the numerical solution of second-order ODEs. One technique to obtain more accurate integration process is to construct linear multi-step methods with hybrid points employing future solution values. In this regard, we construct families of Stӧrmer-Cowell type hybrid SSILMMs having higher order than that of the symmetric super-implicit method recently proposed for the same step number using the Taylors series approach. The newly derived hybrid SSILMMs are p-stable with accurate results when tested on some special second order IVPs.
VL  - 3
IS  - 3
ER  -

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Author Information

Oluwasegun Micheal Ibrahim

Department of Mathematical Sciences, African Institute for Mathematical Sciences, Kigali City, Rwanda; Advance Research Laboratory, Department of Mathematics, University of Benin, Benin City, Nigeria
Monday Ndidi Oziegbe Ikhile

Advance Research Laboratory, Department of Mathematics, University of Benin, Benin City, Nigeria

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Plain Text BibTeX RIS

APA Style

Oluwasegun Micheal Ibrahim, Monday Ndidi Oziegbe Ikhile. (2017). Highly Stable Super-Implicit Hybrid Methods for Special Second Order IVPs. American Journal of Applied Scientific Research, 3(3), 21-27. https://doi.org/10.11648/j.ajasr.20170303.11

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ACS Style

Oluwasegun Micheal Ibrahim; Monday Ndidi Oziegbe Ikhile. Highly Stable Super-Implicit Hybrid Methods for Special Second Order IVPs. Am. J. Appl. Sci. Res. 2017, 3(3), 21-27. doi: 10.11648/j.ajasr.20170303.11

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AMA Style

Oluwasegun Micheal Ibrahim, Monday Ndidi Oziegbe Ikhile. Highly Stable Super-Implicit Hybrid Methods for Special Second Order IVPs. Am J Appl Sci Res. 2017;3(3):21-27. doi: 10.11648/j.ajasr.20170303.11

Copy | Download

@article{10.11648/j.ajasr.20170303.11,
  author = {Oluwasegun Micheal Ibrahim and Monday Ndidi Oziegbe Ikhile},
  title = {Highly Stable Super-Implicit Hybrid Methods for Special Second Order IVPs},
  journal = {American Journal of Applied Scientific Research},
  volume = {3},
  number = {3},
  pages = {21-27},
  doi = {10.11648/j.ajasr.20170303.11},
  url = {https://doi.org/10.11648/j.ajasr.20170303.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajasr.20170303.11},
  abstract = {The idea of symmetric super-implicit linear multi-step methods (SSILMMs) necessitates the use of not just past and present solution values of the ordinary differential equations (ODEs), but also, future values of the solution. Such methods have been proposed recently for the numerical solution of second-order ODEs. One technique to obtain more accurate integration process is to construct linear multi-step methods with hybrid points employing future solution values. In this regard, we construct families of Stӧrmer-Cowell type hybrid SSILMMs having higher order than that of the symmetric super-implicit method recently proposed for the same step number using the Taylors series approach. The newly derived hybrid SSILMMs are p-stable with accurate results when tested on some special second order IVPs.},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - Highly Stable Super-Implicit Hybrid Methods for Special Second Order IVPs
AU  - Oluwasegun Micheal Ibrahim
AU  - Monday Ndidi Oziegbe Ikhile
Y1  - 2017/10/31
PY  - 2017
N1  - https://doi.org/10.11648/j.ajasr.20170303.11
DO  - 10.11648/j.ajasr.20170303.11
T2  - American Journal of Applied Scientific Research
JF  - American Journal of Applied Scientific Research
JO  - American Journal of Applied Scientific Research
SP  - 21
EP  - 27
PB  - Science Publishing Group
SN  - 2471-9730
UR  - https://doi.org/10.11648/j.ajasr.20170303.11
AB  - The idea of symmetric super-implicit linear multi-step methods (SSILMMs) necessitates the use of not just past and present solution values of the ordinary differential equations (ODEs), but also, future values of the solution. Such methods have been proposed recently for the numerical solution of second-order ODEs. One technique to obtain more accurate integration process is to construct linear multi-step methods with hybrid points employing future solution values. In this regard, we construct families of Stӧrmer-Cowell type hybrid SSILMMs having higher order than that of the symmetric super-implicit method recently proposed for the same step number using the Taylors series approach. The newly derived hybrid SSILMMs are p-stable with accurate results when tested on some special second order IVPs.
VL  - 3
IS  - 3
ER  -

Copy | Download