Pseudospectral method is an alternative of finite differences and finite elements method to solve nonlinear partial differential equations (PDEs), especially in nonlinear waves. The Pseudospectal method is very efficient because it use the fast fourier transform to calculate discrete Fourier transform in the algorithm. In this paper, the Pseudospectral scheme is modified by adding the linear damping effect and de-aliasing technique, and has been tested in Ostrovsky equation, where Ostrovsky equation is a modified of Korteweg-de Vries equation with an addition of background Earth’s rotation. The addition of the linear damping is to prevent the possibility of radiated waves re-entering from the boundaries and disturbing the main wave structure. Most of the numerical simulations occur with the aliasing errors due to pollution of numerically calculated Fourier transform by higher frequencies component because of the truncation of the series. To prevent this, the de-aliasing technique is implemented on the nonlinear term and linear damping region by setting of the amplitudes to be zero at the end of both boundaries. Therefore, the simulation results of Pseudospectral method will be smooth without any high frequency errors even for the high amplitude of the waves from initial condition.

Floating structures, such as Spar platform, are likely to experience significant motions while operation due to Vortex-induced Motion (VIM). The main features of VIM include aspect ratio and mass ratio of the structure. This paper focuses on further development of a previously published semi-empirical method called wake oscillator model (WOM) for VIM, which aims to derive a mathematical correlation in modelling all features of the phenomenon. Analytical solution is proposed to coupled WOM and structure oscillator model based on the Van der Pol equation by integrating mass ratio, m* = 4.36, and various low aspect ratios between 0.3 and 2.0. Additionally, a new approach was initiated to embed several empirical parameters linked to the aspect ratio in the existing WOM. It was found the aspect ratio parameter in the modified WOM significantly affected the performance of the model for estimation of VIM on floating structures.

Explorations by oil and gas companies have moved from shallow to deep water to satisfy consumers' changing needs. A circular- shaped cylinder structure placed in deep water is also known spar platform, is normally floated and subjected to severe conditions which cause unpleasant motions and fatigue damage to the structure. Wake oscillator model is considered a semi-empirical model that is most suitable for the evaluation of Vortexinduced Vibrations (VIV) structure features during the design stage. This work focuses on validation of wake oscillator model for VIV with previously semi-empirical method. Wake oscillator and structure oscillator models are coupled based on the Van der Pol Equation. The coupled models were evaluated and analytically validated. The results showed a qualitative and quantitative agreement with previous analytical, at the same maximum peak amplitude response,

This paper discusses the development and the analytical solution of a mathematical model based on drug release system from a swelling delivery device. The mathematical model is represented by a one-dimensional advection-diffusion equation with nonhomogeneous moving boundary condition. The solution procedures consist of three major steps. Firstly, the application of steady state solution method, which is used to transform the nonhomogeneous moving boundary condition to homogeneous boundary condition. Secondly, the application of the Landau transformation technique that gives a significant impact in removing the advection term in the system of equation and transforming the moving boundary condition to a fixed boundary condition. Thirdly, the used of separation of variables method to find the analytical solution for the resulted initial boundary value problem. The results show that the swelling rate of delivery device and drug release rate is influenced by value of growth factor r.