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Highly Stable Super-Implicit Hybrid Methods for Special Second Order IVPs
American Journal of Applied Scientific Research
Volume 3, Issue 3, May 2017, Pages: 21-27
Received: Jun. 29, 2017; Accepted: Jul. 14, 2017; Published: Oct. 31, 2017
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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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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.
Super-Implicit, Hybrid LMM, Stӧrmer-Cowell Method, P-stability
To cite this article
Oluwasegun Micheal Ibrahim, Monday Ndidi Oziegbe Ikhile, Highly Stable Super-Implicit Hybrid Methods for Special Second Order IVPs, American Journal of Applied Scientific Research. Vol. 3, No. 3, 2017, pp. 21-27. doi: 10.11648/j.ajasr.20170303.11
Copyright © 2017 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License ( which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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