FIFTH-ORDER A(α)-STABLE BLOCK HYBRID ADAMS-MOULTON METHOD FOR SOLUTIONS OF PREDATOR-PREY AND LORENZ SYSTEMS

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.

Keywords

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