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1.
The steady laminar boundary layer flow over a permeable flat plate in a uniform free stream, with the bottom surface of the plate is heated by convection from a hot fluid is considered. Similarity solutions for the flow and thermal fields are possible if the mass transpiration rate at the surface and the convective heat transfer from the hot fluid on the lower surface of the plate vary like x−1/2, where x is the distance from the leading edge of the solid surface. The governing partial differential equations are first transformed into ordinary differential equations, before being solved numerically. The effects of the governing parameters on the flow and thermal fields are thoroughly examined and discussed.  相似文献
2.
Series Solutions of Systems of Nonlinear Fractional Differential Equations   总被引:1,自引:0,他引:1  
Differential equations of fractional order appear in many applications in physics, chemistry and engineering. An effective and easy-to-use method for solving such equations is needed. In this paper, series solutions of the FDEs are presented using the homotopy analysis method (HAM). The HAM provides a convenient way of controlling the convergence region and rate of the series solution. It is confirmed that the HAM series solutions contain the Adomian decomposition method (ADM) solution as special cases.   相似文献
3.
Solving systems of ODEs by homotopy analysis method   总被引:1,自引:0,他引:1  
This paper applies the homotopy analysis method (HAM) to systems of ordinary differential equations (ODEs). The systems investigated include stiff systems, the chaotic Genesio system and the matrix Riccati-type differential equation. The HAM gives approximate analytical solutions which are of comparable accuracy to the seven- and eight-order Runge–Kutta method (RK78).  相似文献
4.
A hierarchical structure for on-line steady-state optimizingcontrol of interconnected systems is discussed which utilizesthe available mathematical model more efficiently than in previoustechniques, in spite of large model-reality differences. Thestructure is of an iterative type and uses both the mathematicalmodel of the system and the system output measurements. Thestructure produces a control which satisfies necessary optimalityconditions, provided that the system mathematical model is point-parametric.Several iterative strategies for finding a solution are presented.The strategies are compared with respect to their applicability,the total number of set-point changes needed to find solution,and the amount of information exchanged between control unitsand process during iterations.  相似文献
5.
In this paper, a convergence proof of the Adomian decomposition method (ADM) applied to the generalized nonlinear Burgers–Huxley equation is presented. The decomposition scheme obtained from the ADM yields an analytical solution in the form of a rapidly convergent series. The direct symbolic–numeric scheme is shown to be efficient and accurate.  相似文献
6.
In this paper, the Adomian decomposition method (ADM) is applied to the famous Lorenz system. The ADM yields an analytical solution in terms of a rapidly convergent infinite power series with easily computable terms. Comparisons between the decomposition solutions and the fourth-order Runge–Kutta (RK4) numerical solutions are made for various time steps. In particular we look at the accuracy of the ADM as the Lorenz system changes from a non-chaotic system to a chaotic one.  相似文献
7.
The effect of suction/injection on the laminar mixed convectionboundary-layer flow about a vertical wall in an incompressibleviscous fluid is considered. The similarity solutions are obtainedfor some values of the suction/injection parameter as well asthe mixed convection parameter for three particular cases: uniformtemperature, uniform heat flux and stagnation flow. The resultingsystem of non-linear ordinary differential equations is solvednumerically for both assisting and opposing flow regimes usinga finite-difference scheme known as the Keller box method. Numericalresults are obtained for the skin friction coefficient and localNusselt number as well as velocity and temperature profiles.The effects of the involved parameters on the skin frictioncoefficient and the local Nusselt number characteristics arediscussed. It is found that dual solutions exist for assistingflow, besides that usually reported in the literature for opposingflow.  相似文献
8.
We consider distribution results for closed orbits of the partially hyperbolic system: an ergodic toral automorphism à with respect to a (G, )–extension A. In particular we obtain an analogue of the Chebotarev theorem in this situation which is an asymptotic formula for the number of closed orbits of the base transformation according to how they lift onto the extension space. To arrive at this result we introduce a cyclic extension  of A and deduce that  and A is essentially a group extension and homogeneous extension of à respectively. This observation of a group extension is similar to the setting previously studied by Parry & Pollicott and using the prime orbit theorem of Waddington we then derive at an auxiliary result for the group extension analogoues to Parry & Pollicott. Finally we relate this auxiliary result to the homogeneous extension by resorting to the work of Noorani & Parry.  相似文献
9.
This paper introduces the picture problem which is the analogue of the word problem, one dimension higher. Then the existence of a finite connected 3-complex with unsolvable picture problem is shown.AMS Subject Classification (1991): 20F10, 20E6.  相似文献
10.
The characteristics of steady two-dimensional laminar boundary layer flow of a viscous and incompressible fluid past a moving wedge with suction or injection are theoretically investigated. The transformed boundary layer equations are solved numerically using an implicit finite-difference scheme known as the Keller-box method. The effects of Falkner-Skan power-law parameter (m), suction/injection parameter (f0) and the ratio of free stream velocity to boundary velocity parameter (λ) are discussed in detail. The numerical results for velocity distribution and skin friction coefficient are given for several values of these parameters. Comparisons with the existing results obtained by other researchers under certain conditions are made. The critical values off 0,m and λ are obtained numerically and their significance on the skin friction and velocity profiles is discussed. The numerical evidence would seem to indicate the onset of reverse flow as it has been found by Riley and Weidman in 1989 for the Falkner-Skan equation for flow past an impermeable stretching boundary.  相似文献
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