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A Class of Hybrid Multistep Block Methods with A –Stability for the Numerical Solution of Stiff Ordinary Differential Equations

Author

Listed:
  • Zarina Bibi Ibrahim

    (Dept of Mathematics, Faculty of Science, Serdang 43400 UPM, Malaysia)

  • Amiratul Ashikin Nasarudin

    (Institute for Mathematical Research, Dept of Mathematics, Faculty of Science, Serdang 43400 UPM, Malaysia)

Abstract

Recently, block backward differentiation formulas (BBDFs) are used successfully for solving stiff differential equations. In this article, a class of hybrid block backward differentiation formulas (HBBDFs) methods that possessed A –stability are constructed by reformulating the BBDFs for the numerical solution of stiff ordinary differential equations (ODEs). The stability and convergence of the new method are investigated. The methods are found to be zero-stable and consistent, hence the method is convergent. Comparisons between the proposed method with exact solutions and existing methods of similar type show that the new extension of the BBDFs improved the stability with acceptable degree of accuracy.

Suggested Citation

  • Zarina Bibi Ibrahim & Amiratul Ashikin Nasarudin, 2020. "A Class of Hybrid Multistep Block Methods with A –Stability for the Numerical Solution of Stiff Ordinary Differential Equations," Mathematics, MDPI, vol. 8(6), pages 1-19, June.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:6:p:914-:d:367346
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    References listed on IDEAS

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    1. Ramos, Higinio & Singh, Gurjinder, 2017. "A tenth order A-stable two-step hybrid block method for solving initial value problems of ODEs," Applied Mathematics and Computation, Elsevier, vol. 310(C), pages 75-88.
    2. S. A. M. Yatim & Z. B. Ibrahim & K. I. Othman & M. B. Suleiman, 2011. "A Quantitative Comparison of Numerical Method for Solving Stiff Ordinary Differential Equations," Mathematical Problems in Engineering, Hindawi, vol. 2011, pages 1-12, September.
    3. I. S. M. Zawawi & Z. B. Ibrahim & F. Ismail & Z. A. Majid, 2012. "Diagonally Implicit Block Backward Differentiation Formulas for Solving Ordinary Differential Equations," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2012, pages 1-8, November.
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    Cited by:

    1. Qureshi, Sania & Ramos, Higinio & Soomro, Amanullah & Akinfenwa, Olusheye Aremu & Akanbi, Moses Adebowale, 2024. "Numerical integration of stiff problems using a new time-efficient hybrid block solver based on collocation and interpolation techniques," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 220(C), pages 237-252.

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