Non-Hybrid Continuous Multistep Method For Block Extended Second Derivative Backward Differentiation Formula

Authors

  • A. I. Bakari Department of Mathematics, Federal University, Dutse, Nigeria Author
  • Sunday Babuba Department of Mathematics, Federal University, Dutse, Nigeria Author

DOI:

https://doi.org/10.60787/tnamp.v21.485

Keywords:

Backward Differentiation formula, Second Derivative, Collocation, Interpolation, Non-Hybrid, Block Method

Abstract

This research paper, the solution of stiff problems by non- hybrid continuous multistep method for block extended second derivative backward differentiation formula is presented. The scheme was constructed through interpolation and collocation concept. The derived method is tested and region of absolute stability is also verified. The approximate solution indicates that to be efficient with better accuracy when compared with other authors’ results. 

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References

Skwame, Y., Kumleng, G.M.& Bakari., I.A: (2017) Second derivative hybrid block backward Differentiation formulae for numerical solution of stiff systems. Journal of Advances in Mathematics and Computer Sciences.25 (3): 1-11.

Bakari., I.A., Skwame, & Y. Kumleng, G.M: (2018) Implicit hybrid block Six- Step backward, Differentiation formula for the solution of stiff Ordinary Differential Equations International Journal of Mathematics and Statistics Invention Volume 6 Issue3, PP 45-51.

Majid.Z.A and Suleiman. M: (2006). Direct integration implicit variable steps method for solving Higher Order systems of ordinary differential equations directly. Sains Malaysiana. 35(2)

Kayode, S.J. and Adeyeye, O. (2011) A 3-Step Hybrid Method for Direct Solution of Second Order Initial Value Problems. Australian Journal of basic and Applied Sciences, 5, 2121-2126.

Olabode, B.T. (2007). Some Linear Multistep Methods for Special and General third Orde Initial Value Problems of Ordinary Differential Equation, PhD Thesis, Federal University Technology, Akure. (Unpublished).

Ehigie, J.O., Okunuga, S. A., & Sofoluwe, A. B. (2011). 3-point block methods for directintegration of general second-order ordinary differential equations. Advances in Numerical Analysis.10:1– 14.

Milne, W.E. (1953). Numerical solution of differential equations. 19(3). New York: Wiley

Skwame, Y., Dalatu, P.I., Sabo, J. & Mathew, M. (2019). Numerical application of third derivative hybrid block methods on third order initial value problem of ordinary differential equations. International Journal of Statistics and Applied Mathematics. 4(6), 90-100.

Skwame, Y., Sabo, J. Tumba. P. and Kyagya. (2017). Order Ten Implicit One-Step Hybrid Block Method for Solution of Stiff Second Order Ordinary Differential Equations. IJEAS. 4, 65-72.

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Published

2025-03-01

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Section

Articles

How to Cite

Non-Hybrid Continuous Multistep Method For Block Extended Second Derivative Backward Differentiation Formula. (2025). The Transactions of the Nigerian Association of Mathematical Physics, 21, 133-142. https://doi.org/10.60787/tnamp.v21.485

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