A wavelet approximation method for solving nonlinear ship roll damping equations: An operational matrix of derivative approach

Abstract

The effect of roll damping on ship dynamics is more significant. Here, an efficient Lucas wavelet method is applied to estimate the parameters of ship roll motion models. For the first time, a learning model was approached for forecasting over ship roll angle with damping and restoring moments where the results are obtained from Lucas wavelet method. A barge-like vessel fitted with two spherical tank models and FPSO tank model equations with different damping and restoring coefficients are investigated to estimate the validity and applicability of the proposed LWM for different loading conditions. With the help of operational matrices of derivatives, the nonlinear differential equations are converted into a system of algebraic equations using an appropriate collocation point. The proposed wavelet approximation results are compared with experimental data, frozen cargo, Runge-Kutta method of 4th order (RKM) and Homotopy Perturbation Method (HPM) results. Moreover, numerical experiments are provided to show that the proposed wavelet method is an effective and convenient method for solving nonlinear differential equations in ship dynamics.