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151.
A fourth‐order compact finite difference scheme on the nine‐point 2D stencil is formulated for solving the steady‐state Navier–Stokes/Boussinesq equations for two‐dimensional, incompressible fluid flow and heat transfer using the stream function–vorticity formulation. The main feature of the new fourth‐order compact scheme is that it allows point‐successive overrelaxation (SOR) or point‐successive underrelaxation iteration for all Rayleigh numbers Ra of physical interest and all Prandtl numbers Pr attempted. Numerical solutions are obtained for the model problem of natural convection in a square cavity with benchmark solutions and compared with some of the accurate results available in the literature. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
152.
In this paper,the authors obtain the Backlund transformation on time-like surfaces with constant mean curvature in R2,1.Using this transformation,families of surfaces with constant mean curvature from known ones can be constructed. 相似文献
153.
本文讨论延迟微分方程单支方法的非线性稳定性 .对于 Kα,β,γ类非线性延迟微分方程 ,我们证明带有线性插值的 G( c,p,q) -代数稳定的单支方法当 c≤ 1时是 GR( p/2 ,q/2 ) -稳定及弱 GAR( p/2 ,q/2 ) -稳定的 ,当 c<1时是 GAR( p/2 ,q/2 ) -稳定的 .最后的数值试验表明了上述结论的正确性 . 相似文献
154.
Bruzón M. S. Gandarias M. L. Muriel C. Ramírez J. Saez S. Romero F. R. 《Theoretical and Mathematical Physics》2003,137(1):1367-1377
We use the classical and nonclassical methods to obtain symmetry reductions and exact solutions of the (2+1)-dimensional integrable Calogero–Bogoyavlenskii–Schiff equation. Although this (2+1)-dimensional equation arises in a nonlocal form, it can be written as a system of differential equations and, in potential form, as a fourth-order partial differential equation. The classical and nonclassical methods yield some exact solutions of the (2+1)-dimensional equation that involve several arbitrary functions and hence exhibit a rich variety of qualitative behavior. 相似文献
155.
Piotr Bogusaw Mucha Witold Sadowski 《Mathematical Methods in the Applied Sciences》2005,28(15):1867-1880
The paper analyses long time behaviour of solutions of the Navier–Stokes equations in a two‐dimensional pipe‐like domain. The system is studied with perfect slip boundary conditions with arbitrary inflow conditions at infinity. The main results show the existence of global in time solutions and of an attractor for the dynamical system generated by the model. The paper also establishes an upper bound for the Hausdorff dimension of the attractor. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
156.
In this paper we consider an obstacle control problem where the state satisfies a quasilinear elliptic variational inequality and the control function is the obstacle. The state is chosen to be close to the desire profile while the H2 norms of the obstacle is not too large. Existence and necessary conditions for the optimal control are established. 相似文献
157.
Dynamic systems described by nonlinear differential equations of the second order are studied. It is assumed that certain
preliminary information on the dissipative or elastic characteristics of systems is known. A new approach is demonstrated
to obtaining full information on unknown or partially known characteristics of a system from measurements of not only displacements
but also velocities and accelerations
__________
Published in Prikladnaya Mekhanika, Vol. 41, No. 6, pp. 139–143, June 2005. 相似文献
158.
We use a symmetry approach to solve the classification problem for integrable N-component evolution systems having the form of conservation laws. We obtain complete lists of both isotropic and anisotropic systems of this type and find auto-Bäcklund transformations with a spectral parameter for all systems. 相似文献
159.
L. Fatone M. C. Recchioni F. Zirilli 《Journal of Optimization Theory and Applications》2004,121(2):223-257
In this paper, we consider furtivity and masking problems in time-dependent three-dimensional electromagnetic obstacle scattering. That is, we propose a criterion based on a merit function to minimize or to mask the electromagnetic field scattered by a bounded obstacle when hit by an incoming electromagnetic field and, with respect to this criterion, we drive the optimal strategy. These problems are natural generalizations to the context of electromagnetic scattering of the furtivity problem in time-dependent acoustic obstacle scattering presented in Ref. 1. We propose mathematical models of the furtivity and masking time-dependent three-dimensional electromagnetic scattering problems that consist in optimal control problems for systems of partial differential equations derived from the Maxwell equations. These control problems are approached using the Pontryagin maximum principle. We formulate the first-order optimality conditions for the control problems considered as exterior problems defined outside the obstacle for systems of partial differential equations. Moreover, the first-order optimality conditions derived are solved numerically with a highly parallelizable numerical method based on a perturbative series of the type considered in Refs. 2–3. Finally, we assess and validate the mathematical models and the numerical method proposed analyzing the numerical results obtained with a parallel implementation of the numerical method in several experiments on test problems. Impressive speedup factors are obtained executing the algorithms on a parallel machine when the number of processors used in the computation ranges between 1 and 100. Some virtual reality applications and some animations relative to the numerical experiments can be found in the website http://www.econ.unian.it/recchioni/w10/. 相似文献
160.
Leibniz agebras are a generalization of Lie algebras, where no symmetry properties of the bracket are required. In this Letter we introduce a notion of R-matrices for this structure and the related Yang–Baxter equations, and discuss some of their basic properties. 相似文献