scholarly journals Finite difference schemes for long-time integration

1994 ◽  
Vol 114 (2) ◽  
pp. 265-279 ◽  
Author(s):  
Zigo Haras ◽  
Shlomo Ta'asan
2016 ◽  
Vol 19 (4) ◽  
pp. 1015-1041 ◽  
Author(s):  
Hailiang Liu ◽  
Terrance Pendleton

AbstractThe purpose of this paper is to develop and test novel invariant-preserving finite difference schemes for both the Camassa-Holm (CH) equation and one of its 2-component generalizations (2CH). The considered PDEs are strongly nonlinear, admitting soliton-like peakon solutions which are characterized by a slope discontinuity at the peak in the wave shape, and therefore suitable for modeling both short wave breaking and long wave propagation phenomena. The proposed numerical schemes are shown to preserve two invariants, momentum and energy, hence numerically producing wave solutions with smaller phase error over a long time period than those generated by other conventional methods. We first apply the scheme to the CH equation and showcase the merits of considering such a scheme under a wide class of initial data. We then generalize this scheme to the 2CH equation and test this scheme under several types of initial data.


JSIAM Letters ◽  
2011 ◽  
Vol 3 (0) ◽  
pp. 37-40 ◽  
Author(s):  
Yuto Miyatake ◽  
Takayasu Matsuo ◽  
Daisuke Furihata

2021 ◽  
Vol 13 (4) ◽  
pp. 701 ◽  
Author(s):  
Binbin Wang ◽  
Hao Cha ◽  
Zibo Zhou ◽  
Bin Tian

Clutter cancellation and long time integration are two vital steps for global navigation satellite system (GNSS)-based bistatic radar target detection. The former eliminates the influence of direct and multipath signals on the target detection performance, and the latter improves the radar detection range. In this paper, the extensive cancellation algorithm (ECA), which projects the surveillance channel signal in the subspace orthogonal to the clutter subspace, is first applied in GNSS-based bistatic radar. As a result, the clutter has been removed from the surveillance channel effectively. For long time integration, a modified version of the Fourier transform (FT), called long-time integration Fourier transform (LIFT), is proposed to obtain a high coherent processing gain. Relative acceleration (RA) is defined to describe the Doppler variation results from the motion of the target and long integration time. With the estimated RA, the Doppler frequency shift compensation is carried out in the LIFT. This method achieves a better and robust detection performance when comparing with the traditional coherent integration method. The simulation results demonstrate the effectiveness and advantages of the proposed processing method.


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