Eight-order second derivative block linear multistep method for chaotic initial value problems

Abstract

This paper aims to enhance the accuracy and stability of eight-order second derivative linear multistep methods (LMMs) for solving chaotic initial value problems (IVPs). The method is developed using a multistep collocation approach. The newly derived method is applied to plot solution curves, solid lines, and phase portraits, which are compared with those obtained from
well-established ordinary differential equations (ODEs) solvers. The results show excellent agreement between the proposed method and the established solvers. The proposed block method demonstrates efficiency and accuracy, making it a suitable choice for solving chaotic and nonlinear ordinary differential equations.