Abstract In this research work, we proposed a Haar wavelet collocation method (HWCM) for the numerical solution of first- and second-order nonlinear hyperbolic equations. The time derivative in governing equations is approximated by finite difference. equation converted into its full algebraic form once space derivatives are replaced series. Convergence analysis performed both time, where compu...

This abstract is concerned with the development of an efficient and scalable hybrid-spectral model for a fully nonlinear numerical wave tank with finite dimensions, which is used for simulation of nonlinear free surface waves generated by a moving wavemaker. The approach pursued here is based on the OceanWave3D strategy established in [1, 6, 7], replacing the horisontal high order finite differ...

We consider the stochastic model of concentrated Liquid Crystal Polymers(LCPs) in the plane Couette flow. The dynamic equation for the liquid crystal polymers is described by a nonlinear stochastic differential equation with Maier-Saupe interaction potential. The stress tensor is obtained from an ensemble average of microscopic polymer configurations. We present the local existence and uniquene...

One of the primary ways to enhance heat transfer rate is to use extended surfaces or fins. The heat transfer mechanism of fin is to conduct heat from the heat source to fin surface by its thermal conduction, and then dissipates it to surrounding medium by convection. Most common application areas of fins are in combustion engines, heat exchangers and cooling of electronic equipments. Early stud...

In this paper we discuss the optimal liquidation over a finite time horizon until the exit time. The drift and diffusion terms of the asset price are general functions depending on all variables including control and market regime. There is also a local nonlinear transaction cost associated to the liquidation. The model deals with both the permanent impact and the temporary impact in a regime s...

In this article, we put a direct method to construct the rational solitary wave solutions for some nonlinear differential difference equations in mathematical physics which may be called the rational solitary wave difference method. We use the proposed method to construct the rational solitary exact solutions for some nonlinear differential difference equations via the lattice equation, the dis...