共查询到20条相似文献,搜索用时 31 毫秒
1.
In this paper, we propose a regularized version of the generalized
NCP-function proposed by Hu, Huang and Chen [J. Comput. Appl. Math., 230 (2009),
pp. 69-82]. Based on
this regularized function, we propose a semismooth Newton method for
solving nonlinear complementarity problems, where a non-monotone
line search scheme is used. In particular, we show that the proposed
non-monotone method is globally and locally superlinearly
convergent under suitable assumptions. We test the
proposed method by solving the test problems from MCPLIB.
Numerical experiments indicate that this algorithm has better
numerical performance in the case of $p=5$ and $\theta\in[0.25,075]$ than other cases. 相似文献
2.
本文考虑了分布阶时间分数阶扩散波动方程,其中时间分数阶导数是在Caputo意义上定义的,其阶次$\alpha,\beta$分别属于(0,1)和(1,2).文中提出了在计算上行之有效的数值方法来模拟分布阶时间分数阶扩散波动方程.在时间上,通过中点求积公式把分布阶项转换为多项的时间分数阶导数项,并且利用$L1$和$L2$公式来近似Caputo分数阶导数;空间上使用Galerkin有限元方法进行离散.给出了基于$H^1$范数的有限元解的稳定性和误差估计的详细证明,最后的数值算例结果说明了理论分析的正确性以及有效性. 相似文献
3.
《Applied Mathematics Letters》2006,19(8):712-720
In the current work, the authors present a symbolic algorithm for finding the inverse of any general nonsingular tridiagonal matrix. The algorithm is mainly based on the work presented in [Y. Huang, W.F. McColl, Analytic inversion of general tridiagonal matrices, J. Phys. A 30 (1997) 7919–7933] and [M.E.A. El-Mikkawy, A fast algorithm for evaluating nth order tridiagonal determinants, J. Comput. Appl. Math. 166 (2004) 581–584]. It removes all cases where the numeric algorithm in [Y. Huang, W.F. McColl, Analytic inversion of general tridiagonal matrices, J. Phys. A 30 (1997) 7919–7933] fails. The symbolic algorithm is suited for implementation using Computer Algebra Systems (CAS) such as MACSYMA, MAPLE and MATHEMATICA. An illustrative example is given. 相似文献
4.
Matheus J. Lazo Delfim F. M. Torres 《Journal of Optimization Theory and Applications》2013,156(1):56-67
Derivatives and integrals of noninteger order were introduced more than three centuries ago but only recently gained more attention due to their application on nonlocal phenomena. In this context, the Caputo derivatives are the most popular approach to fractional calculus among physicists, since differential equations involving Caputo derivatives require regular boundary conditions. Motivated by several applications in physics and other sciences, the fractional calculus of variations is currently in fast development. However, all current formulations for the fractional variational calculus fail to give an Euler–Lagrange equation with only Caputo derivatives. In this work, we propose a new approach to the fractional calculus of variations by generalizing the DuBois–Reymond lemma and showing how Euler–Lagrange equations involving only Caputo derivatives can be obtained. 相似文献
5.
Considering the features of the fractional Klein-Kramers equation (FKKE) in phase space, only the unilateral boundary condition
in position direction is needed, which is different from the bilateral boundary conditions in [Cartling B., Kinetics of activated
processes from nonstationary solutions of the Fokker-Planck equation for a bistable potential, J. Chem. Phys., 1987, 87(5),
2638–2648] and [Deng W., Li C., Finite difference methods and their physical constrains for the fractional Klein-Kramers equation,
Numer. Methods Partial Differential Equations, 2011, 27(6), 1561–1583]. In the paper, a finite difference scheme is constructed,
where temporal fractional derivatives are approximated using L1 discretization. The advantages of the scheme are: for every temporal level it can be dealt with from one side to the other
one in position direction, and for any fixed position only a tri-diagonal system of linear algebraic equations needs to be
solved. The computational amount reduces compared with the ADI scheme in [Cartling B., Kinetics of activated processes from
nonstationary solutions of the Fokker-Planck equation for a bistable potential, J. Chem. Phys., 1987, 87(5), 2638–2648] and
the five-point scheme in [Deng W., Li C., Finite difference methods and their physical constrains for the fractional Klein-Kramers
equation, Numer. Methods Partial Differential Equations, 2011, 27(6), 1561–1583]. The stability and convergence are proved
and two examples are included to show the accuracy and effectiveness of the method. 相似文献
6.
The properties of oscillating cuspoid integrals whose phase functions are odd and even polynomials are investigated. These integrals are called oddoids and evenoids, respectively (and collectively, oddenoids). We have studied in detail oddenoids whose phase functions contain up to three real parameters. For each oddenoid, we have obtained its Maclaurin series representation and investigated its relation to Airy–Hardy integrals and Bessel functions of fractional orders. We have used techniques from singularity theory to characterise the caustic (or bifurcation set) associated with each oddenoid, including the occurrence of complex whiskers. Plots and short tables of numerical values for the oddenoids are presented. The numerical calculations used the software package CUSPINT [N.P. Kirk, J.N.L. Connor, C.A. Hobbs, An adaptive contour code for the numerical evaluation of the oscillatory cuspoid canonical integrals and their derivatives, Comput. Phys. Commun. 132 (2000) 142–165]. 相似文献
7.
Some well-known L-type formulae, i.e., L1, L1-2, and L1-2-3 formulae,
are usually employed to approximate the Caputo fractional derivative of order α ∈
(0, 1). In this paper, we aim to elaborate on the stability and convergence analyses
of some finite difference methods (FDMs) for solving the subdiffusion equation, i.e.,
a diffusion equation which exploits the Caputo time-fractional derivative of order $α$.
In fact, the FDMs considered here are based on the usual central difference scheme
for the spatial derivative, and the Caputo derivative is approximated by using methods such as the L1, L1-2, and L1-2-3 formulae. Thanks to a specific type of the
discrete version of the Gronwall inequality, we show that the FDMs are unconditionally stable in the maximum norm and also discrete $H^1$ norm. Then, we prove that
the finite difference method which uses the L1, L1-2, and L1-2-3 formulae has the
global order of convergence $2−α$, $3−α$, and 3, respectively. Finally, some numerical
tests confirm the theoretical results. A brief conclusion finishes the paper. 相似文献
8.
The block-by-block method, proposed by Linz for a kind of Volterra integral equations with nonsingular kernels, and extended by Kumar
and Agrawal to a class of initial value problems of fractional
differential equations (FDEs) with Caputo derivatives, is an
efficient and stable scheme. We analytically prove and numerically
verify that this method is convergent with order at least 3 for any
fractional order index $\alpha>0$. 相似文献
9.
A time fractional functional differential equation driven by the fractional Brownian motion 下载免费PDF全文
Let $B^H$ be a fractional Brownian motion with Hurst index $H>\frac12$. In this paper, we prove the global existence and uniqueness of the equation
$$
\begin{cases}
^CD_t^{\gamma}x(t)=f(x_t)+G(x_t)\frac{d}{dt}B^H(t),\ \ \ \ &t\in(0,T], \x(t)=\eta(t), \ \ \ \ \ &t\in[-r,0],
\end{cases}
$$
where $\max\{H,2-2H\}<\gamma<1$, $^CD_t^{\gamma}$ is the Caputo derivative, and $x_t\in \mathcal{C}_r=\mathcal{C}([-r,0],\mathbb{R})$ with $x_t(u)=x(t+u),u\in[-r,0]$. We also study the dependence of the solution on the initial condition. 相似文献
10.
The convergence to steady state solutions of the Euler equations for weighted compact nonlinear schemes (WCNS) [Deng X. and Zhang H. (2000), J. Comput. Phys. 165, 22-44 and Zhang S., Jiang S. and Shu C.-W. (2008), J. Comput. Phys. 227, 7294-7321] is studied through numerical tests. Like most other shock capturing schemes, WCNS also suffers from the problem that the residue can not settle down to machine zero for the computation of the steady state solution which contains shock waves but hangs at the truncation error level. In this paper, the techniques studied in [Zhang S. and Shu. C.-W. (2007), J. Sci. Comput. 31, 273-305 and Zhang S., Jiang S and Shu. C.-W. (2011), J. Sci. Comput. 47, 216-238], to improve the convergence to steady state solutions for WENO schemes, are generalized to the WCNS. Detailed numerical studies in one and two dimensional cases are performed. Numerical tests demonstrate the effectiveness of these techniques when applied to WCNS. The residue of various order WCNS can settle down to machine zero for typical cases while the small post-shock oscillations can be removed. 相似文献
11.
In this paper, we develop a two-grid method (TGM) based on the FEM for 2D nonlinear time fractional two-term mixed sub-diffusion and diffusion wave equations. A two-grid algorithm is proposed for solving the nonlinear system, which consists of two steps: a nonlinear FE system is solved on a coarse grid, then the linearized FE system is solved on the fine grid by Newton iteration based on the coarse solution. The fully discrete numerical approximation is analyzed, where the Galerkin finite element method for the space derivatives and the finite difference scheme for the time Caputo derivative with order $\alpha\in(1,2)$ and $\alpha_{1}\in(0,1)$. Numerical stability and optimal error estimate $O(h^{r+1}+H^{2r+2}+\tau^{\min\{3-\alpha,2-\alpha_{1}\}})$ in $L^{2}$-norm are presented for two-grid scheme, where $t,$ $H$ and $h$ are the time step size, coarse grid mesh size and fine grid mesh size, respectively. Finally, numerical experiments are provided to confirm our theoretical results and effectiveness of the proposed algorithm. 相似文献
12.
Man-Chung Yeung 《高等学校计算数学学报(英文版)》2012,5(3):447-492
With the aid of index functions, we re-derive the ML($n$)BiCGStab algorithm
in [Yeung and Chan, SIAM J. Sci. Comput., 21 (1999), pp. 1263-1290] systematically.
There are $n$ ways to define the ML($n$)BiCGStab residual vector. Each definition leads
to a different ML($n$)BiCGStab algorithm. We demonstrate this by presenting a second
algorithm which requires less storage. In theory, this second algorithm serves as a
bridge that connects the Lanczos-based BiCGStab and the Arnoldi-based FOM while
ML($n$)BiCG is a bridge connecting BiCG and FOM. We also analyze the breakdown
situation from the probabilistic point of view and summarize some useful properties of
ML($n$)BiCGStab. Implementation issues are also addressed. 相似文献
13.
14.
Stability results and existence theorems for nonlinear delay-fractional differential equations with $\varphi^*_p$-operator 下载免费PDF全文
The study of delay-fractional differential equations (fractional DEs) have recently attracted a lot of attention from scientists working on many different subjects dealing with mathematically modeling. In the study of fractional DEs the first question one might raise is whether the problem has a solution or not. Also, whether the problem is stable or not? In order to ensure the answer to these questions, we discuss the existence and uniqueness of solutions (EUS) and Hyers-Ulam stability (HUS) for our proposed problem, a nonlinear fractional DE with $p$-Laplacian operator and a non zero delay $\tau>0$ of order $n-1<\nu^*,\,\epsilon相似文献
15.
本文主要研究了一类多项Caputo分数阶随机微分方程的Euler-Maruyama (EM)方法,并证明了其强收敛性.具体地,我们首先构造了求解多项Caputo分数阶随机微分方程初值问题的EM方法,然后证明分数阶导数的指标满足$\frac{1}{2}<\alpha_{1}<\alpha_{2}<\cdots<\alpha_{m}<1$时,该方法是$\alpha_{m}-\alpha_{m-1}$阶强收敛的.文末的数值试验验证了理论结果的正确性. 相似文献
16.
Xin Wen LSEC ICMSEC Academy of Mathematics Systems Science Chinese Academy of Sciences Beijing China 《计算数学(英文版)》2009,(4):474-483
In this paper we give proof of three binomial coefficient inequalities. These inequalities are key ingredients in [Wen and Jin, J. Comput. Math. 26, (2008), 1-22] to establish the L^1-error estimates for the upwind difference scheme to the linear advection equations with a piecewise constant wave speed and a general interface condition, which were further used to establish the L^1-error estimates for a Hamiltonian-preserving scheme developed in [Jin and Wen, Commun. Math. Sci. 3, (2005), 285-315] to the Liouville equation with piecewise constant potentials [Wen and Jin, SIAM J. Numer. Anal. 46, (2008), 2688-2714]. 相似文献
17.
本文中,我们对茅德康在【D.K.Mao,Towards front-tracking based on conservation in two space dimensionsⅡ,tracking discontinuities in capturing fashion,J.Comput.Phys.,226,(2007),pp 1550-1588】一文中所建立的守恒型跟踪法进行了改进,成功将算法运用到多介质流体界面的计算中.最后,我们使用改进后的算法计算了两个数值算例,验证了算法的有效性. 相似文献
18.
In Cheb-Terrab and Roche (Comput Phys Commun 130(1–2):204–231, 2000) a classification of the Abel equations known as solvable
in the literature was presented. In this paper, we show that all the integrable rational Abel differential equations that
appear in Cheb-Terrab and Roche (Comput Phys Commun 130(1–2):204–231, 2000) and consequently in Cheb-Terrab and Roche (Eur
J Appl Math 14(2):217–229, 2003) can be reduced to a Riccati differential equation or to a first-order linear differential
equation through a change with a rational map. The change is given explicitly for each class. Moreover, we have found a unified
way to find the rational map from the knowledge of the explicitly first integral. 相似文献
19.
As the generalization of the integer order partial differential equations (PDE), the fractional order PDEs are drawing more and more attention for their applications in fluid flow, finance and other areas. This paper presents high-order accurate Runge-Kutta local discontinuous Galerkin (DG) methods for one- and two-dimensional fractional diffusion equations containing derivatives of fractional order in space. The Caputo derivative is chosen as the representation of spatial derivative, because it may represent the fractional derivative by an integral operator. Some numerical examples show that the convergence orders of the proposed local $P^k$-DG methods are $O(h^{k+1})$ both in one and two dimensions, where $P^k$ denotes the space of the real-valued polynomials with degree at most $k$. 相似文献
20.
The nonadjacent form method of Koblitz [Advances in Cryptology (CRYPTO'98), in: Lecture Notes in Comput. Sci., vol. 1462, 1998, pp. 327–337] is an efficient algorithm for point multiplication on a family of supersingular curves over a finite field of characteristic 3. In this paper, a further discussion of the method is given. A window nonadjacent form method is proposed and its validity is proved. Efficient reduction and pre-computations are given. Analysis shows that more than 30% of saving can be achieved. 相似文献