Wavelet based spectral algorithm for nonlinear dynamical systems arising in ship dynamics

In this paper, we have applied an efficient shifted second kind Chebyshev wavelet method (S2KCWM) to vibrating dynamical models arising in mechanical systems such as vibration of circular membrane, damped spring mass system and ship oscillatory motions. To the best of our knowledge, until now there is no rigorous wavelet based solution has been reported for the vibrating dynamical models. The power of the manageable method is confirmed. The wavelet solutions are compared with numerical simulations by MATLAB. Good agreement between the solutions is presented in this paper. Some numerical examples are given to demonstrate the validity and applicability of the proposed method. Moreover the use of Chebyshev wavelets is found to be simple, efficient, flexible, convenient, less computation costs and computationally attractive.