Real life phenomena found in various fields such as engineering, physics,
biology and communication theory can be modeled as nonlinear higher order ordinary
differential equations, particularly the Duffing oscillator. Analytical solutions for these
differential equations can be time consuming whereas, conventional numerical solutions
may lack accuracy. This research propose a block multistep method integrated with a
variable order step size (VOS) algorithm for solving these Duffing oscillators directly.
The proposed VOS Block method provides an alternative numerical solution by reducing
computational cost (time) but without loss of accuracy. Numerical simulations
are compared with known exact solutions for proof of accuracy and against current
numerical methods for proof of efficiency (steps taken).