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An operator splitting method is proposed for the Degasperis-Procesi (DP) equation, by which the DP equation is decomposed into the Burgers equation and the Benjamin-Bona-Mahony (BBM) equation. Then, a second-order TVD scheme is applied for the Burgers equation, and a linearized implicit finite difference method is used for the BBM equation. Furthermore, the Strang splitting approach is used to construct the solution in one time step. The numerical solutions of the DP equation agree with exact solutions, e.g. the multipeakon solutions very well. The proposed method also captures the formation and propagation of shockpeakon solutions, and reveals wave breaking phenomena with good accuracy.

The technology of On-line hot roll grinding (ORG, for short) is one of new technologies of hot strip mill appearing in recent years. It is distinctly for on-line roll grinding technology to increase quality of production and efficiency of producing, and save energy. Therefore, studying and applying ORG technologies is paid more attention to by iron and steel corporations. Many ORG technologies adopt the type of end-face grinding to rehabilitate hot rolls online. However, few studies have been done on the grinding mechanism for this grinding mode. In this paper, some grinding mechanisms of end-face cylindrical grinding with cup-shaped CBN resin wheel are studied from the point of grinding geometry. The equation is deduced to calculate the contact length. The characters of contact length are studied.

The discrete singular convolution (DSC) algorithm is applied to the Korteweg-de Vries (KdV) and modified KdV (mKdV) equations with a particular emphasis on a comparison with the Fourier pseudospectral (FPS) method. The errors of the DSC algorithm with respect to the numerical resolution are investigated by using the discrete Fourier analysis. The numerical results indicate that the DSC method can be more accurate than the FPS method for many nonlinear wave problems that are non-bandlimited in nature.