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61.
Aboubakari Traore Benjamin Mampassi Bisso Saley 《Central European Journal of Mathematics》2007,5(4):751-763
In this paper we consider the problem of detecting pollution in some non linear parabolic systems using the sentinel method.
For this purpose we develop and analyze a new approach to the discretization which pays careful attention to the stability
of the solution. To illustrate convergence properties we give some numerical results that present good properties and show
new ways for building discrete sentinels.
相似文献
62.
Zhimin Zhang. 《Mathematics of Computation》2005,74(252):1621-1636
Superconvergence phenomenon of the Legendre spectral collocation method and the -version finite element method is discussed under the one dimensional setting. For a class of functions that satisfy a regularity condition (M): on a bounded domain, it is demonstrated, both theoretically and numerically, that the optimal convergent rate is supergeometric. Furthermore, at proper Gaussian points or Lobatto points, the rate of convergence may gain one or two orders of the polynomial degree.
63.
谈高校基础实验室仪器设备配置的几个问题 总被引:1,自引:0,他引:1
本文提出高校物理实验室,仪器设备购置中应注意的几条原则。并提出一套估算办法。 相似文献
64.
Quantitative predictions of the behavior of many deterministic systems are uncertain due to ubiquitous heterogeneity and insufficient characterization by data. We present a computational approach to quantify predictive uncertainty in complex phenomena, which is modeled by (partial) differential equations with uncertain parameters exhibiting multi-scale variability. The approach is motivated by flow in random composites whose internal architecture (spatial arrangement of constitutive materials) and spatial variability of properties of each material are both uncertain. The proposed two-scale framework combines a random domain decomposition (RDD) and a probabilistic collocation method (PCM) on sparse grids to quantify these two sources of uncertainty, respectively. The use of sparse grid points significantly reduces the overall computational cost, especially for random processes with small correlation lengths. A series of one-, two-, and three-dimensional computational examples demonstrate that the combined RDD–PCM approach yields efficient, robust and non-intrusive approximations for the statistics of diffusion in random composites. 相似文献
65.
Harendra Singh Fahimeh Akhavan Ghassabzadeh Emran Tohidi Carlo Cattani 《Mathematical Methods in the Applied Sciences》2020,43(9):5941-5952
In this paper, the Legendre spectral collocation method (LSCM) is applied for the solution of the fractional Bratu's equation. It shows the high accuracy and low computational cost of the LSCM compared with some other numerical methods. The fractional Bratu differential equation is transformed into a nonlinear system of algebraic equations for the unknown Legendre coefficients and solved with some spectral collocation methods. Some illustrative examples are also given to show the validity and applicability of this method, and the obtained results are compared with the existing studies to highlight its high efficiency and neglectable error. 相似文献
66.
Suruchi Singh Swarn Singh 《Numerical Methods for Partial Differential Equations》2020,36(5):1028-1043
A high order modified nodal bi-cubic spline collocation method is proposed for numerical solution of second-order elliptic partial differential equation subject to Dirichlet boundary conditions. The approximation is defined on a square mesh stencil using nine grid points. The solution of the method exists and is unique. Convergence analysis has been presented. Moreover, the superconvergent phenomena can be seen in proposed one step method. The numerical results clearly exhibit the superiority of the new approximation, in terms of both accuracy and computational efficiency. 相似文献
67.
Nuri Murat Yağmurlu Ali Sercan Karakaş 《Numerical Methods for Partial Differential Equations》2020,36(5):1170-1183
In this article, the equal width (EW) equation is going to be solved numerically. In order to show the accuracy of the presented method, six test problems namely single solitary wave, interaction of two solitary waves, interaction of three solitary waves, Maxwellian initial condition, undular bore, and soliton collision are going to be solved. For the first test problem, since it has exact solution, the error norms L2 and L∞ are going to be calculated and compared with some of the earlier studies existing in the literature. Moreover, the three invariants I1, I2, and I3 of the given problems during the simulations are calculated and tabulated. Besides those comparisons, the relative changes of the invariants are given. Finally, a comparison of those error norms and invariants has clearly shown that the present approach obtained compatible and better results than most of the earlier works by using the same parameters. 相似文献
68.
Based on the generalized Laguerre and Hermite functions, we construct two types of Birkhoff-type interpolation basis functions. The explicit expressions are derived, and fast and stable algorithms are provided for computing these basis functions. As applications, some well-conditioned collocation methods are proposed for solving various second-order differential equations in unbounded domains. Numerical experiments illustrate that our collocation methods are more efficient than the standard Laguerre/Hermite collocation approaches. 相似文献
69.
In this article, we discuss the superconvergence of the interpolated collocation solutions for Hammerstein equations. Applying this new interpolation postprocessing to the collocation approximation xh, we get a higher accuracy approximation I xh, whose convergence order is the same as that of the iterated collocation method. Such an interpolation postprocessing method is much simpler. Also, numerical experiments are shown to demonstrate the efficiency of the interpolation postprocessing method. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010 相似文献
70.
Berna Bülbül Mustafa Gülsu Mehmet Sezer 《Numerical Methods for Partial Differential Equations》2010,26(5):1006-1020
The aim of this article is to present an efficient numerical procedure for solving nonlinear integro‐differential equations. Our method depends mainly on a Taylor expansion approach. This method transforms the integro‐differential equation and the given conditions into the matrix equation which corresponds to a system of nonlinear algebraic equations with unkown Taylor coefficients. The reliability and efficiency of the proposed scheme are demonstrated by some numerical experiments and performed on the computer program written in Maple10. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010 相似文献