Pseudospecteral method with linear damping effect and de-aliasing technique in solving nonlinear PDEs

Abstract

Abstract 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.