Abstract
Roll motion is one of the key motions related to a vessel’s dynamic stability. It is essential for the dynamic stability of ships in the realistic sea. For this research study, we have investigated the parameters involved in damping of the ship. In general, mathematical modelling of the rolling response of a ship can be formulated by the linear, nonlinear, and fractional differential equations because the amplitude of oscillation is increased. An efficient Genocchi polynomial approximation method (GPAM) is successfully applied for the biased ship roll motion model. The basic idea of the collocation method together with the operational matrices of derivatives used for nonlinear differential equation and convert it into a system of algebraic equations. The convergence and error analysis of the proposed method are also discussed. A few numerical experiments are carried out for some specific and important types of problems including the biased roll motion equations. The results are compared to those produced using the Legendre wavelet method (LWM) and the homotopy perturbation method (HPM). It is observed that the proposed spectral algorithm is robust, accurate, and easy to apply.