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A variational formulation of the vertically-integrated differential equations for free surface wave motion is presented. A finite element model is derived for solving this nonlinear system of hydrodynamic equations. The time integration scheme employed is discussed and the results obtained demonstrate its good stability and accuracy.Several applications of the model are considered: the first problem is an open channel of uniform depth and the second an open channel of linearly varying depth. The ‘inflow’ boundary condition is prescribed in terms of the velocity which represents a wavemaker and/or a flow source, while the ‘outflow’ boundary condition is specified in terms of the water elevation. The outflow condition is adjusted for two cases, a reflecting boundary (finite channel) and a non-reflecting boundary (open-ended channel). The latter boundary condition is examined in some detail and the results obtained show that the numerical model can produce the non-reflecting boundary that is similar to the analytical radiation condition for waves. Computational results for a third problem, involving wave reflection from a submerged cylinder, are also presented and compared with both experimental data and analytical predictions.The simplicity and the performance of the computational model suggest that free surface waves can be simulated without excessively complicated numerical schemes. The ability of the model to simulate outflow boundary conditions properly is of special importance since these conditions present serious problems for many numerical algorithms. 相似文献
135.
We use nondiscrete mathematical induction to extend the applicability of the Secant methods for solving equations in a Banach setting. Our approach has the following advantages over earlier works under the same information: weaker sufficient convergence conditions; tighter error bounds on the distances involved and more information on the location of the solution. Numerical examples where our results apply but earlier ones fail to solve nonlinear equation as well as tighter error bounds are also provided in this study. 相似文献
136.
Antonio Morante 《International Journal of Mathematical Education in Science & Technology》2013,44(7):936-949
We exhibit a simple model of a plane landing that involves only basic concepts of differential calculus, so it is suitable for a first-year calculus lab. We use the computer algebra system Maxima and the interactive geometry software GeoGebra to do the computations and graphics. 相似文献
137.
随着网络行为同社会行为联系的进一步密切,网络攻击的最终目的越来越多地落在获取具体的经济意义上.病毒制造者和传播者在巨大利益的驱使下,利用木马技术进行各种网络盗窃、诈骗活动.计算机网络病毒传播模型是研究计算机网络病毒的手段和工具之一,根据木马病毒的特点,建立了木马病毒的数学模型,研究了影响病毒传播的参数及对应措施. 相似文献
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L.Venkateswara Reddy R.N. Mukherjee 《Journal of Mathematical Analysis and Applications》1999,240(2):37
In this paper, a generalized ratio invexity concept has been applied for single objective fractional programming problems. A concept which has been invoked seems to be more general than the one used earlier by Khan and Hanson in such contexts. Further, duality results for fractional programs have also been obtained. 相似文献
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Michio Umino 《The Journal of mathematical sociology》2013,37(4):237-246
This paper examines Dawes (1975) model on commons dilemma (CD) situation and proposes an alternative model which formulates CD. Firstly, it makes clear that Dawes model does not have the characteristics of CD. Secondly, it specifies “resource unit condition” which models of commons dilemma must satisfy. Thirdly, it presents CD model, which is obtained by setting the condition in Dawes model. And lastly, it examines some nature of the proposed model and find that in CD situation, fine is distributed proportionally to each player's property. 相似文献