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Numerical solutions for generalized Rosenau equation are considered and two energy conservative finite difference schemes are proposed. Existence of the solutions for the difference scheme has been shown. Stability, convergence, and priori error estimate of the scheme are proved using energy method. Numerical results demonstrate that two schemes are efficient and reliable.

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This paper presents a modulus stretch-based circular Synthetic Aperture Radar (SAR) imaging method. This method improves the traditional backprojection algorithm for circular SAR imaging, and introduces the modulus stretch transformation function in the imaging process. By performing a modulus stretch transformation on the intermediate results, the target contour in the final imaging result is thinner and clearer. A thinner and clearer contour can help to increase the recognizability of the target and provide a basis for subsequent target recognition. The proposed method is demonstrated on the line target imaging simulations and Gothca dataset.

With a more concise condition for the ordered parameter groups, some nonlinear weakly singular integral inequalities of Wendroff type, which generalize some existing results, are established. Furthermore, application examples in the boundedness and uniqueness of the solution of a singular partial integral equation are given.