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81.
Pradip Roul V. M. K. Prasad Goura Roberto Cavoretto 《Numerical Methods for Partial Differential Equations》2023,39(1):45-64
This paper presents an efficient numerical technique for solving a class of time-fractional diffusion equation. The time-fractional derivative is described in the Caputo form. The L1 scheme is used for discretization of Caputo fractional derivative and a collocation approach based on sextic B-spline basis function is employed for discretization of space variable. The unconditional stability of the fully-discrete scheme is analyzed. Two numerical examples are considered to demonstrate the accuracy and applicability of our scheme. The proposed scheme is shown to be sixth order accuracy with respect to space variable and (2 − α)-th order accuracy with respect to time variable, where α is the order of temporal fractional derivative. The numerical results obtained are compared with other existing numerical methods to justify the advantage of present method. The CPU time for the proposed scheme is provided. 相似文献
82.
具有逐项分数阶导数的微分方程边值问题解的存在性 总被引:1,自引:0,他引:1
研究了一类具有逐项分数阶导数的微分方程边值问题.对参数的各种取值情况进行了全面的分析,运用Banach压缩映射原理和Schauder不动点定理,得到并证明了边值问题解的存在性定理.最后,给出了两个例子来证明结论有效. 相似文献
83.
关于拉格朗日乘数法的几何意义 总被引:1,自引:0,他引:1
利用梯度和方向导数的概念讨论函数在曲线或曲面上的变化率,从而给出拉格朗日乘数法的一个直观的几何解释. 相似文献
84.
Xin Liu Lili Chen Yanfeng Zhao Xianhua Song 《Mathematical Methods in the Applied Sciences》2022,45(1):77-92
In this paper, the problem of the uniform stability for a class of fuzzy fractional-order genetic regulatory networks with random discrete delays, distributed delays, and parameter uncertainties is studied. Although there is a portion of literature on using fixed point theorems to study the stability of fractional neural networks, most of them required the fractional order to be in . However, the case of the fractional-order belonging to has not been discussed. To solve it, this work proposes a novel idea of using fixed point theory to study the stability of fuzzy (0,1) order neural networks, the problem of the uniqueness of the solution of the considered genetic regulatory networks is resolved, and a novel sufficient condition to guarantee the uniform stability of above genetic regulatory networks is also derived. Eventually, an example is given to demonstrate that the obtained result is effective. 相似文献
85.
由于分段三次参数Hermite插值的切矢往往被作为变量,故可对其进行优化以使得构造的插值曲线满足特定的要求.为了构造兼具保形性与光顺性的平面分段三次参数Hermite插值曲线,给出了一种通过同时极小化导数振荡和应变能来确定切矢的方法.首先以导数振荡函数和应变能函数为双目标建立了切矢满足的方程系统;然后证明了方程系统存在唯一解,并给出了解的具体表达式;最后给出了误差分析,并通过数值算例表明方法的有效性.结果表明,相对于导数振荡极小化方法和应变能极小化方法,所提出的导数振荡和应变能极小化方法同时兼顾了平面分段三次参数Hermite插值曲线的保形性和光顺性. 相似文献
86.
87.
On Finite Element Approximations to a Shape Gradient Flow in Shape Optimization of Elliptic Problems
Chunxiao Liu & Shengfeng Zhu 《计算数学(英文版)》2023,41(5):957-980
Shape gradient flows are widely used in numerical shape optimization algorithms. We investigate the accuracy and effectiveness of approximate shape gradients flows for shape optimization of elliptic problems. We present convergence analysis with a priori error estimates for finite element approximations of shape gradient flows associated with a distributed or boundary expression of Eulerian derivative. Numerical examples are presented to verify theory and show that using the volume expression is effective for shape optimization with Dirichlet and Neumann boundary conditions. 相似文献
88.
设Bm(f,·)为函数f在d维单纯形σ上的n阶Bernstein多项式,本文对f∈Cr(σ)及f∈Cr+2(σ)给出了f的各阶编导数用Bn(f,·)相应偏导数逼近的误差估计.同时也考虑了整系数Bernstein多项式的Lp模估计 相似文献
89.
Alexander G. Ramm Alexandra B. Smirnova Angelo Favini 《Annali di Matematica Pura ed Applicata》2003,182(1):37-52
A nonlinear operator equation F(x)=0, F:H→H, in a Hilbert space is considered. Continuous Newton’s-type procedures based on a construction of a dynamical system with
the trajectory starting at some initial point x
0 and becoming asymptotically close to a solution of F(x)=0 as t→+∞ are discussed. Well-posed and ill-posed problems are investigated.
Received: June 29, 2001; in final form: February 26, 2002?Published online: February 20, 2003
This paper was finished when AGR was visiting Institute for Theoretical Physics, University of Giessen. The author thanks
DAAD for support 相似文献
90.
A Global Solution to a
Two-dimensional Riemann Problem Involving Shocks as Free
Boundaries 总被引:4,自引:0,他引:4
YuxiZheng 《应用数学学报(英文版)》2003,19(4):559-572
We present a global solution to a Riemann problem for the pressure gradient system of equations.The Riemann problem has initially two shock waves and two contact discontinuities. The angle between the two shock waves is set initially to be close to 180 degrees. The solution has a shock wave that is usually regarded as a free boundary in the self-similar variable plane. Our main contribution in methodology is handling the tangential oblique derivative boundary values. 相似文献