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991.
John T. Conway 《Integral Transforms and Special Functions》2016,27(8):667-682
A substantial number of new indefinite integrals involving the incomplete elliptic integral of the third kind are presented, together with a few integrals for the other two kinds of incomplete elliptic integral. These have been derived using a Lagrangian method which is based on the differential equations which these functions satisfy. Techniques for obtaining new integrals are discussed, together with transformations of the governing differential equations. Integrals involving products combining elliptic integrals of different kinds are also presented. 相似文献
992.
Suxiang He Xiangfeng Liu Chuanmei Wang 《Numerical Functional Analysis & Optimization》2016,37(6):680-698
This article presents a novel nonlinear Lagrange algorithm for solving minimax optimization problems with both inequality and equality constraints, which eliminates the nonsmoothness of the considered problems and the numerical difficulty of the penalty method. The convergence of the proposed algorithm is analyzed under some mild assumptions, in which the sequence of the generated solutions converges locally to a Karush-Kuhn-Tucker solution at a linear rate when the penalty parameter is less than a threshold and the error bound of the solutions is also obtained. Finally, the detailed numerical results for several typical testproblems are given in order to show the performance of the proposed algorithm. 相似文献
993.
By means of a conjugation scheme based on generalized convex conjugation theory instead of Fenchel conjugation, we build an alternative dual problem, using the perturbational approach, for a general optimization one defined on a separated locally convex topological space. Conditions guaranteeing strong duality for primal problems which are perturbed by continuous linear functionals and their respective dual problems, which is named stable strong duality, are established. In these conditions, the fact that the perturbation function is evenly convex will play a fundamental role. Stable strong duality will also be studied in particular for Fenchel and Lagrange primal–dual problems, obtaining a characterization for Fenchel case. 相似文献
994.
We study functional calculus properties of C0‐groups on real interpolation spaces using transference principles. We obtain interpolation versions of the classical transference principle for bounded groups and of a recent transference principle for unbounded groups. Then we show that each group generator on a Banach space has a bounded ‐calculus on real interpolation spaces. Additional results are derived from this. 相似文献
995.
A cell edge‐based linearity‐preserving scheme for diffusion problems on two‐dimensional unstructured grids
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Longshan Luo Zhiming Gao Jiming Wu 《Mathematical Methods in the Applied Sciences》2017,40(15):5423-5436
We propose a new finite volume scheme for 2D anisotropic diffusion problems on general unstructured meshes. The main feature lies in the introduction of two auxiliary unknowns on each cell edge, and then the scheme has both cell‐centered primary unknowns and cell edge‐based auxiliary unknowns. The auxiliary unknowns are interpolated by the multipoint flux approximation technique, which reduces the scheme to a completely cell‐centered one. The derivation of the scheme satisfies the linearity‐preserving criterion that requires that a discretization scheme should be exact on linear solutions. The resulting new scheme is then called as a cell edge‐based linearity‐preserving scheme. The optimal convergence rates are numerically obtained on unstructured grids in case that the diffusion tensor is taken to be anisotropic and/or discontinuous. Copyright © 2017 John Wiley & Sons, Ltd. 相似文献
996.
New interpolation error estimates and a posteriori error analysis for linear parabolic interface problems
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Jhuma Sen Gupta Rajen Kumar Sinha G. Murali Mohan Reddy Jinank Jain 《Numerical Methods for Partial Differential Equations》2017,33(2):570-598
We derive residual‐based a posteriori error estimates of finite element method for linear parabolic interface problems in a two‐dimensional convex polygonal domain. Both spatially discrete and fully discrete approximations are analyzed. While the space discretization uses finite element spaces that are allowed to change in time, the time discretization is based on the backward Euler approximation. The main ingredients used in deriving a posteriori estimates are new Clément type interpolation estimates and an appropriate adaptation of the elliptic reconstruction technique introduced by (Makridakis and Nochetto, SIAM J Numer Anal 4 (2003), 1585–1594). We use only an energy argument to establish a posteriori error estimates with optimal order convergence in the ‐norm and almost optimal order in the ‐norm. The interfaces are assumed to be of arbitrary shape but are smooth for our purpose. Numerical results are presented to validate our derived estimators. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 570–598, 2017 相似文献
997.
Elimhan N. Mahmudov 《Applicable analysis》2017,96(7):1215-1228
This paper concerns the sufficient conditions of optimality for initial value problem with higher order differential inclusions (HODIs) and free endpoint constraints. Formulation of the transversality conditions plays a substantial role in the next investigations without which hardly any necessary or sufficient conditions would be obtained. In terms of Euler–Lagrange and Hamiltonian forms the sufficient conditions of optimality both for convex and “non-convex” HODIs are based on the apparatus of locally adjoint mappings. Moreover, by applying the main result to a Bolza problem described by a polynomial differential operator with constant coefficients in terms of the adjoint differential operator the sufficient condition of optimality is obtained. 相似文献
998.
将三次样条理论与再生核理论相结合,利用再生核函数巧妙地构造了三次样条函数空间的一组基底.基于三次样条插值的高收敛特点,得到了微分方程边值问题近似解的一种新的求解方法.数值算例展现出算法简单、有效. 相似文献
999.
Spirals are curves of one-signed, monotone increasing or decreasing curvature. Spiral segments have the advantage that the minimum and maximum curvatures are at their endpoints. Two situations where the planar, two-point G2 Hermite interpolation problem can be solved with a pair of rational spiral segments are outlined here. 相似文献
1000.
Let I be a finite or infinite interval and dμ a measure on I. Assume that the weight function w(x)>0, w′(x) exists, and the function w′(x)/w(x) is non-increasing on I. Denote by ℓk's the fundamental polynomials of Lagrange interpolation on a set of nodes x1<x2<<xn in I. The weighted Lebesgue function type sum for 1≤i<j≤n and s≥1 is defined byIn this paper the exact lower bounds of Sn(x) on a “big set” of I and are obtained. Some applications are also given. 相似文献