Implicit stomer cowell k-step hybrid block methods for solution of first order ordinary differential equations (ODEs)

  • Authors

    • AM Badmus POST GRADUATE SCHOOL ,NIGERIAN DEFENCE ACADEMY KADUNA NIGERIA
    • YA Yahaya FEDERAL UNIVERSITY OF TECHNOLOGY MINNA NIGERIA
    • AO Subair NIGERIAN DEFENCE ACADEMY KADUNA NIGERIA
    2014-10-08
    https://doi.org/10.14419/ijamr.v3i4.3403
  • Abstract

    This paper focuses on derivation of two implicit hybrid Block methods at  and one method  at  Each block method produced at  yielded uniform order 5 and 7 respectively, while the Block implicit method at k = 4 produced uniform order 9. The block analysis of all the methods derived shows that they are zero stable, consistent and convergent. The superiority of these methods over some existing one were demonstrated numerically.

    Keywords: Consistent And Convergent, Implicit Block Methods, Uniform Order and Zero Stable.

  • References

    1. DO Awoyemi. A class of Continuous methods for general second order initial value problems in ordinary differential equations. International Journal of computer Mathematics. Volume72. (1999) pages 29-33 http://dx.doi.org/10.1080/00207169908804832.
    2. AM Badmus and DW Mshelia. Some uniform order block method for the solution of first-order ordinary differential equations. Journal of Nigerian Association of Mathematical Physics, 19, (2011), 149-154.
    3. AM Badmus and DW Mshelia Uniform order zero-stable k step methods for initial value problems of ordinary differential equations. Journal of Nigerian Association of Mathematical Physics volume 20, (2012) 65-74.
    4. AM Badmus and ZA Adegboye .Comparison of two new Quade's type hybrid Block methods for solution of ordinary differential equations. Journal of research in Physical Sciences, volume 6 No1 (2010) pages 71-76
    5. AM Badmus, TA Badmos and FE Ekpenyong. Hybrid Implicit Block algorithms for improved performances in the solution of first order initial value problems. Journal of Nigerian Association of Mathematical Physics volume 23, (2013) pages 95-102
    6. JD Lamber Computational Methods in Ordinary Differential Equations. John Wiley and Sons, New York. (1973) 278
    7. MR Odekunle, AO Adesanya and J Sunday. Four point block method for direct integration of first order ordinary differential equations. International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 Vol. 2, (2012a) pp.1182-1187.
    8. MR Odekunle, AO Adesanya and J Sunday. A new block integrator for the solution of initial value problems of first- order ordinary differential equations. International Journal of Pure and Applied Science and Technology, 11(2), (2012b), 92-100.
    9. AO Subair. A 3- and 4-Step Collocation Hybrid Block Method for Solution of First Order Ordinary Differential Equations". MSc thesis (unpublished) Nigeria Defence Academy Kaduna. (2014),
    10. YA Yahaya. And ZA Adegboye. A New Quade's Type 4-step blocks Hybrid Multistep Method for Accurate and Efficient Parallel Solution of Ordinary Differential Equations. Abacus 34, No 2B: (2007) 271-278.
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  • How to Cite

    Badmus, A., Yahaya, Y., & Subair, A. (2014). Implicit stomer cowell k-step hybrid block methods for solution of first order ordinary differential equations (ODEs). International Journal of Applied Mathematical Research, 3(4), 464-472. https://doi.org/10.14419/ijamr.v3i4.3403

    Received date: 2014-08-19

    Accepted date: 2014-09-14

    Published date: 2014-10-08