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1.
In this article, we construct and analyze a residual-based a posteriori error estimator for a quadratic finite volume method (FVM) for solving nonlinear elliptic partial differential equations with homogeneous Dirichlet boundary conditions. We shall prove that the a posteriori error estimator yields the global upper and local lower bounds for the norm error of the FVM. So that the a posteriori error estimator is equivalent to the true error in a certain sense. Numerical experiments are performed to illustrate the theoretical results. 相似文献
2.
We investigate a (2+1)-dimensional shallow water wave equation and describe its nonlinear dynamical behaviors in physics. Based on the N-soliton solutions, the higher-order fissionable and fusionable waves, fissionable or fusionable waves mixed with soliton molecular and breather waves can be obtained by various constraints of special parameters. At the same time, by the long wave limit method, the interaction waves between fissionable or fusionable waves with higher-order lumps are acquired. Combined with the dynamic figures of the waves, the properties of the solution are deeply studied to reveal the physical significance of the waves. 相似文献
3.
Yang Yang Ying Jiang Prof. Dr. Wei Du Prof. Dr. Ying-Chun Chen 《Chemistry (Weinheim an der Bergstrasse, Germany)》2020,26(8):1754-1758
Isobenzofulvene species are versatile synthons in organic chemistry, which have been employed in diverse challenging higher-order cycloaddition reactions. Here, the first chemoselective and asymmetric cross [10+2] cycloaddition reaction between activated 2-alkylidene-1-indanones and a variety of electron-deficient alkenes has been developed, relying on the in situ generation of dearomative 1-hydroxyl isobenzofulvene anion intermediates under the catalysis of a newly designed bulky cinchona-derived phase-transfer compound. An array of fused frameworks with multifunctionalities were generally furnished in excellent diastereo- and enantioselectivity, even at 1 mol % catalyst loadings. 相似文献
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Yongshuai Zhang Xiangxing Tao Tengteng Yao Jingsong He 《Studies in Applied Mathematics》2020,145(4):812-827
Based on the inverse scattering method, the formulae of one higher-order pole solitons and multiple higher-order poles solitons of the nonlinear Schrödinger equation (NLS) equation are obtained. Their denominators are expressed as , where is a matrix frequently constructed for solving the Riemann-Hilbert problem, and the asterisk denotes complex conjugate. We take two methods for proving is invertible. The first one shows matrix is equivalent to a self-adjoint Hankel matrix , proving . The second one considers the block-matrix form of , proving . In addition, we prove that the dimension of is equivalent to the sum of the orders of pole points of the transmission coefficient and its diagonal entries compose a set of basis. 相似文献
6.
Christopher C. Tisdell 《International Journal of Mathematical Education in Science & Technology》2017,48(5):794-801
Knowing an equation has a unique solution is important from both a modelling and theoretical point of view. For over 70 years, the approach to learning and teaching ‘well posedness’ of initial value problems (IVPs) for second- and higher-order ordinary differential equations has involved transforming the problem and its analysis to a first-order system of equations. We show that this excursion is unnecessary and present a direct approach regarding second- and higher-order problems that does not require an understanding of systems. 相似文献
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本文用全纯函数表示微分方程△f(x,y)-λ(~2)f(x,y)=0的一般解,粮据全纯函数的Bekya积分表示法,建立了复数域内的边界积分方程并针对各种边界条件下Reissner型夹层板、Hoff型夹层板进行了数值求解。 相似文献
9.
本文就薄板后屈曲问题建立一组新型的边界元计算公式,用这组公式求解能方便处理各种边界问题,另外文中将面内应力分解成基本部份和附加部份,并利用微分算子分解理论导得了挠度的一个不同形式的基本解,由于计算公式中,实现了面内位移和挠度的解耦,从而使迭代过程得到简化,文末还对圆板后屈曲路径进行了计算,得到了满意的结果。 相似文献
10.
本文对边界元方法中的各类积分根据其奇异性作分类,并对主值积分的收敛条件、变量替换等进行了讨论,又给出了变替换附加项显式。文中提供的主值积分配项消奇术在边界元方法中是有普遍意义的。 相似文献