Fifth-order A(α)-stable block hybrid adams-moulton method for solutions of predator-prey and Lorenz Systems

Authors

  • Oludare Adedire Department of Mathematics, University of Jos, Plateau, Nigéria
  • Paul C. Mordi Department of Mathematics and Statistics, University of Windsor, Ontario, Canada

DOI:

https://doi.org/10.22481/intermaths.v5i1.14889

Keywords:

hybrid, interpolation, multistep, collocation, matrix-inversion.

Abstract

Problems associated with nonlinearity in predator-prey and chaotic nature embedded in Lorenz system place a significant challenge on numerical methods for their solutions. Some numerical methods may become unstable as step size increases. In this study, a fifth-order A(alpha )-stable (alpha = 89.90 ) k-step block hybrid Adams-Moulton method (BHAMM) was derived incorporating 16/9 as an off-step interpolation point using multistep collocation and matrix inversion technique. Choice of the off-step point of the BHAMM was in the upper part of interval of interpolation points. It was shown that the derived block method was consistent and zero-stable hence a convergent block method. Numerical simulations of predator-prey and Lorenz systems with the newly derived k=3 BHAMM indicated that it was adequate and compared well with Matlab ode23s.

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Published

2024-06-30

How to Cite

Adedire, O. ., & Mordi, P. C. (2024). Fifth-order A(α)-stable block hybrid adams-moulton method for solutions of predator-prey and Lorenz Systems. INTERMATHS, 5(1), 1-9. https://doi.org/10.22481/intermaths.v5i1.14889

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