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91.
In this paper, we study the P-stability of the continuous Runge-Kutta Nystroem method for solving the delayed second order differential equation that does not depend on y′. A general theorem is presented which can be used to obtain complete characterizations of the P-stability regions of these continuous RungeKutta- Nystroem methods. We use the condition to two given RKN methods. 相似文献
92.
93.
94.
A high-order leap-flog based non-dissipative discontinuous Galerkin timedomain method for solving Maxwell's equations is introduced and analyzed. The proposed method combines a centered approximation for the evaluation of fluxes at the interface between neighboring elements, with a Nth-order leap-frog time scheme. Moreover, the interpolation degree is defined at the element level and the mesh is refined locally in a non-conforming way resulting in arbitrary level hanging nodes. The method is proved to be stable under some CFL-like condition on the time step. The convergence of the semi-discrete approximation to Maxwell's equations is established rigorously and bounds on the global divergence error are provided. Numerical experiments with highorder elements show the potential of the method. 相似文献
95.
Tsachouridis Vassilios A.; Kouvaritakis Basil 《IMA Journal of Mathematical Control and Information》2005,22(4):517-540
** Email: vassilios.tsachouridis{at}ieee.org*** Email: basil.kouvaritakis{at}eng.ox.ac.uk Algebraic quadratic equations are a special case of a singlegeneralized algebraic quadratic matrix equation (GQME). Hence,the importance of that equation in science and engineering isevident. This paper focus on the study of solutions of thatGQME and a unified framework for the characterization and identificationof solutions at infinity and of finite solutions of generalquadratic algebraic matrix equations is presented. The analysisis based on the concept of homogeneous projective transformationfor general polynomial systems (Morgan, 1986). In addition,a numerical error analysis for the computed solutions is providedfor the assessment of numerical accuracy, stability and conditioningof the computed solutions. The proposed framework is independentof any numerical method and therefore it can be used along withvarious possible numerical methods for the GQME solution, especiallymatrix flow-based algorithms (Chu, 1994) (e.g. continuation/homotopy,Morgan, 1989). 相似文献
96.
S. E. Zhelezovskii 《Siberian Mathematical Journal》2005,46(2):293-304
We consider the Cauchy problem in a Hilbert space for a second-order abstract quasilinear hyperbolic equation with variable operator coefficients and nonsmooth (but Bochner integrable) free term. For this problem, we establish an a priori energy error estimate for the semidiscrete Galerkin method with an arbitrary choice of projection subspaces. Also, we establish some results on existence and uniqueness of an exact weak solution. We give an explicit error estimate for the finite element method and the Galerkin method in Mikhlin form. 相似文献
97.
在赋范空间中给出了集值映射的二阶切集的概念,利用二阶切集,定义了集值映射的二阶切导数。然后,获得了集值向量优化问题弱极小元的两个二阶最优性必要条件。 相似文献
98.
99.
100.
In this paper we give necessary and sufficient conditions for the existence of a C>
0-semigroup in L
1(I) (I real interval) generated by a second-order differential operator when suitable boundary conditions at the endpoints are imposed. 相似文献