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71.
In this article, we implement relatively new analytical techniques, the variational iteration method and the Adomian decomposition method, for solving nonlinear partial differential equations of fractional order. The fractional derivatives are described in the Caputo sense. The two methods in applied mathematics can be used as alternative methods for obtaining analytic and approximate solutions for different types of fractional differential equations. In these schemes, the solution takes the form of a convergent series with easily computable components. Numerical results show that the two approaches are easy to implement and accurate when applied to partial differential equations of fractional order. 相似文献
72.
Shi-ming Zheng 《计算数学(英文版)》2000,(3)
1. IntroductionLetbe a monic complex polynomial of degree n with zeros fi,'' 9 f.. Some authors havestudied the parallel iterations without evaluation of derivatives for simultaneous findingall zeros of f(t) (see [1]--[10]). The famous one is Weierstrass-Durand-Dochev-Kerneriterationwhere xo is the k-th approximation of (i(l 5 i 5 n) andwhich does not require any information of derivatives and was presented independentlyby Weierstrass[7], DurandlZ], Doche.[3] and Ke..e.14). It is well kno… 相似文献
73.
In this paper, we study the diffusive vector disease model with delay. This problem with strong biological background has attracted much research attention. We focus on the existence of traveling wave fronts, and find that there is a moving zone for the transition from the disease-free state to the infective state. To complete the theoretical analysis, we employ the mathematical tools including the monotone iteration technique as well as the upper and lower solution method. 相似文献
74.
Strong convergence theorems for approximation of common fixed points of asymptoticallyφ-quasi-pseudocontractive mappings and asymptoticallyφ-strictly- pseudocontractive mappings are proved in real Banach spaces by using a new compos- ite implicit iteration scheme with errors.The results presented in this paper extend and improve the main results of Sun,Gu and Osilike published on J.Math.Anal. Appl. 相似文献
75.
利普希茨伪紧缩映射下的利普希茨摄动迭代的Bruck公式 总被引:1,自引:0,他引:1
在非线性分析中,处理伪紧缩算子及其变形的解(不动点)存在性和近似性,从而使演化方程的求解已经发展成为一个独立的理论.使用近似不动点技术,采用摄动迭代方法,目的是证明利普希茨伪紧缩映射序列的收敛性.该迭代方法适用于比利普希茨伪紧缩算子更一般的非线性算子以及Bruck迭代法无法证明其收敛性的情况.推广了Chidume和Zegeye的结果. 相似文献
76.
77.
REMARK ON STABILITY OF ISHIKAWA ITERATIVE PROCEDURES 总被引:2,自引:0,他引:2
1 IntroductionandPreliminariesSupposeEisarealBanachspaceandTisaselfmapofE .Supposex0 ∈Eandxn+1=f(T ,xn)definesaniterationprocedurewhichyieldsasequenceofpoints xn ∞n=0 inE .Foranexample ,thefunctioniterationxn+1=f(T ,xn) =Tx0 .SupposeF(T) =x∈E :Tx=x ≠ andthat xn convergess… 相似文献
78.
Considering the fundamental solution of the Laplace equation as the weight function, we give the iterative format for solving the nonhomogeneous Helmholtz equation with variable coefficients. Furthermore, the iteration method of BEM for solving the equation mentioned above is obtained. The numerical example is given in this paper. Finally, the iteration method of BEM mentioned above is compared with the coupled method of BEM that was presented before then by authors. 相似文献
79.
We present an iterative semi-implicit scheme for the incompressible Navier–Stokes equations, which is stable at CFL numbers well above the nominal limit. We have implemented this scheme in conjunction with spectral discretizations, which suffer from serious time step limitations at very high resolution. However, the approach we present is general and can be adopted with finite element and finite difference discretizations as well. Specifically, at each time level, the nonlinear convective term and the pressure boundary condition – both of which are treated explicitly in time – are updated using fixed-point iteration and Aitken relaxation. Eigenvalue analysis shows that this scheme is unconditionally stable for Stokes flows while numerical results suggest that the same is true for steady Navier–Stokes flows as well. This finding is also supported by error analysis that leads to the proper value of the relaxation parameter as a function of the flow parameters. In unsteady flows, second- and third-order temporal accuracy is obtained for the velocity field at CFL number 5–14 using analytical solutions. Systematic accuracy, stability, and cost comparisons are presented against the standard semi-implicit method and a recently proposed fully-implicit scheme that does not require Newton’s iterations. In addition to its enhanced accuracy and stability, the proposed method requires the solution of symmetric only linear systems for which very effective preconditioners exist unlike the fully-implicit schemes. 相似文献
80.
J.H. Adler J. Brannick C. Liu T. Manteuffel L. Zikatanov 《Journal of computational physics》2011,230(17):6647-6663
This paper develops a first-order system least-squares (FOSLS) formulation for equations of two-phase flow. The main goal is to show that this discretization, along with numerical techniques such as nested iteration, algebraic multigrid, and adaptive local refinement, can be used to solve these types of complex fluid flow problems. In addition, from an energetic variational approach, it can be shown that an important quantity to preserve in a given simulation is the energy law. We discuss the energy law and inherent structure for two-phase flow using the Allen–Cahn interface model and indicate how it is related to other complex fluid models, such as magnetohydrodynamics. Finally, we show that, using the FOSLS framework, one can still satisfy the appropriate energy law globally while using well-known numerical techniques. 相似文献