Fifth-order A(α)-stable block hybrid adams-moulton method for solutions of predator-prey and Lorenz Systems
DOI:
https://doi.org/10.22481/intermaths.v5i1.14889Keywords:
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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