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1.
In [10] it is claimed that the set of predicate tautologies of all complete BL‐chains and the set of all standard tautologies (i. e., the set of predicate formulas valid in all standard BL‐algebras) coincide. As noticed in [11], this claim is wrong. In this paper we show that a complete BL‐chain B satisfies all standard BL‐tautologies iff for any transfinite sequence (ai: i ∈ I) of elements of B , the condition ∧i ∈ I (a2i ) = (∧i ∈ I ai)2 holds in B . (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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A matrix rational Lanczos method for model reduction in large‐scale first‐ and second‐order dynamical systems 下载免费PDF全文
In the present paper, we describe an adaptive modified rational global Lanczos algorithm for model‐order reduction problems using multipoint moment matching‐based methods. The major problem of these methods is the selection of some interpolation points. We first propose a modified rational global Lanczos process and then we derive Lanczos‐like equations for the global case. Next, we propose adaptive techniques for choosing the interpolation points. Second‐order dynamical systems are also considered in this paper, and the adaptive modified rational global Lanczos algorithm is applied to an equivalent state space model. Finally, some numerical examples will be given. 相似文献
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M. J. Ludwig Simon Shaw J. R. Whiteman 《Numerical Methods for Partial Differential Equations》2003,19(2):227-253
This is the second in a pair of articles concerned with the adaptive finite element solution of Riessner‐Mindlin thick plates modeled using first‐order shear deformation theory. This article is concerned with enhancing the a posteriori energy‐error estimators developed in Part I in order to accomodate transition elements in the finite element mesh. The resulting estimators are then used in an adaptive finite element model employing transition elements and the subsequent results discussed and compared with those in Part I. A major part of the article is devoted to identifying a novel patch assembly node algorithm for using the ZZ recovery‐type estimator with transition elements. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 19: 227–253, 2003. 相似文献
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This article applies the first‐order system least‐squares (fosls) finite element method developed by Cai, Manteuffel and McCormick to the compressible Stokes equations. By introducing a new dependent velocity flux variable, we recast the compressible Stokes equations as a first‐order system. Then it is shown that the ellipticity and continuity hold for the least‐squares functionals employing the mixture of H?1 and L2, so that the fosls finite element methods yield best approximations for the velocity flux and velocity. © 2001 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 17:689–699, 2001 相似文献
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Paramjeet Singh Kapil K. Sharma 《Numerical Methods for Partial Differential Equations》2010,26(1):107-116
In this article, we continue the numerical study of hyperbolic partial differential‐difference equation that was initiated in (Sharma and Singh, Appl Math Comput 9 ). In Sharma and Singh, the authors consider the problem with sufficiently small shift arguments. The term negative shift and positive shift are used for delay and advance arguments, respectively. Here, we propose a numerical scheme that works nicely irrespective of the size of shift arguments. In this article, we consider hyperbolic partial differential‐difference equation with negative or positive shift and present a numerical scheme based on the finite difference method for solving such type of initial and boundary value problems. The proposed numerical scheme is analyzed for stability and convergence in L∞ norm. Finally, some test examples are given to validate convergence, the computational efficiency of the numerical scheme and the effect of shift arguments on the solution.© 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010 相似文献
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Houde Han Zhongyi Huang Shangyou Zhang 《Numerical Methods for Partial Differential Equations》2013,29(3):961-978
In this article, we propose an iterative method based on the equation decomposition technique ( 1 ) for the numerical solution of a singular perturbation problem of fourth‐order elliptic equation. At each step of the given method, we only need to solve a boundary value problem of second‐order elliptic equation and a second‐order singular perturbation problem. We prove that our approximate solution converges to the exact solution when the domain is a disc. Our numerical examples show the efficiency and accuracy of our method. Our iterative method works very well for singular perturbation problems, that is, the case of 0 < ε ? 1, and the convergence rate is very fast. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013 相似文献
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M. J. Ludwig Simon Shaw J. R. Whiteman 《Numerical Methods for Partial Differential Equations》2003,19(1):44-66
A posteriori error estimation employing both a residual based estimator and a recovery based estimator is discussed. Interest is focused upon the application to Reissner‐Mindlin type thick plates modeled using first‐order shear deformation theory, and our investigation is limited to uniform meshes of bilinear quadrilateral elements. Numerical results for selected test problems are presented for the resulting error estimators and discussed. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 19: 44–66, 2003 相似文献
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Roman Wencel 《Mathematical Logic Quarterly》2012,58(6):449-467
Given a group (G, ·), G?Mm, definable in a first‐order structure $\mathcal {M}=(M,\ldots )Given a group (G, ·), G?Mm, definable in a first‐order structure $\mathcal {M}=(M,\ldots )$ equipped with a dimension function and a topology satisfying certain natural conditions, we find a large open definable subset V?G and define a new topology τ on G with which (G, ·) becomes a topological group. Moreover, τ restricted to V coincides with the topology of V inherited from Mm. Likewise we topologize transitive group actions and fields definable in $\mathcal {M}$. These results require a series of preparatory facts concerning dimension functions, some of which might be of independent interest. 相似文献
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The generalization to gradient vector fields of the classical double‐well, singularly perturbed functionals, where W(ξ) = 0 if and only if ξ = A or ξ = B, and A ? B is a rank‐1 matrix, is considered. Under suitable constitutive and growth hypotheses on W, it is shown that Iε Γ‐converge to where K* is the (constant) interfacial energy per unit area. © 2002 Wiley Periodicals, Inc. 相似文献
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Convergence analysis for second‐order accurate schemes for the periodic nonlocal Allen‐Cahn and Cahn‐Hilliard equations 下载免费PDF全文
Zhen Guan John Lowengrub Cheng Wang 《Mathematical Methods in the Applied Sciences》2017,40(18):6836-6863
In this paper, we provide a detailed convergence analysis for fully discrete second‐order (in both time and space) numerical schemes for nonlocal Allen‐Cahn and nonlocal Cahn‐Hilliard equations. The unconditional unique solvability and energy stability ensures ? 4 stability. The convergence analysis for the nonlocal Allen‐Cahn equation follows the standard procedure of consistency and stability estimate for the numerical error function. For the nonlocal Cahn‐Hilliard equation, because of the complicated form of the nonlinear term, a careful expansion of its discrete gradient is undertaken, and an H ?1 inner‐product estimate of this nonlinear numerical error is derived to establish convergence. In addition, an a priori bound of the numerical solution at the discrete level is needed in the error estimate. Such a bound can be obtained by performing a higher order consistency analysis by using asymptotic expansions for the numerical solution. Following the technique originally proposed by Strang (eg, 1964), instead of the standard comparison between the exact and numerical solutions, an error estimate between the numerical solution and the constructed approximate solution yields an O (s 3+h 4) convergence in norm, in which s and h denote the time step and spatial mesh sizes, respectively. This in turn leads to the necessary bound under a standard constraint s ≤C h . Here, we also prove convergence of the scheme in the maximum norm under the same constraint. 相似文献
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It is shown that the extended version of the Puri-Rubin result given recently by Stadje (1994) is neither new nor the most general available in the literature.
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Mehdi Dehghan Mehrdad Lakestani 《Numerical Methods for Partial Differential Equations》2009,25(4):931-938
A numerical technique is presented for the solution of the second order one‐dimensional linear hyperbolic equation. This method uses the Chebyshev cardinal functions. The method consists of expanding the required approximate solution as the elements of Chebyshev cardinal functions. Using the operational matrix of derivative, the problem is reduced to a set of algebraic equations. Some numerical examples are included to demonstrate the validity and applicability of the technique. The method is easy to implement and produces very accurate results. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009 相似文献
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Dingwen Deng Chengjian Zhang 《Numerical Methods for Partial Differential Equations》2013,29(1):102-130
In this article, a new compact alternating direction implicit finite difference scheme is derived for solving a class of 3‐D nonlinear evolution equations. By the discrete energy method, it is shown that the new difference scheme has good stability and can attain second‐order accuracy in time and fourth‐order accuracy in space with respect to the discrete H1 ‐norm. A Richardson extrapolation algorithm is applied to achieve fourth‐order accuracy in temporal dimension. Numerical experiments illustrate the accuracy and efficiency of the extrapolation algorithm. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013 相似文献
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Tuncay Candan 《Mathematical Methods in the Applied Sciences》2017,40(1):205-209
This paper presents the existence of positive periodic solutions for first‐order neutral differential equation with distributed deviating arguments. We apply Krasnoselskii's fixed point theorem to obtain our results. An example is given to support the theory. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
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In this article, We analyze the ‐version of the discontinuous Galerkin finite element method (DGFEM) for the distributed first‐order linear hyperbolic optimal control problems. We derive a posteriori error estimators on general finite element meshes which are sharp in the mesh‐width . These error estimators are shown to be useful in adaptive finite element approximation for the optimal control problems. For the DGFEM we admit very general irregular meshes. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2011 相似文献
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Santanu Saha Ray 《Numerical Methods for Partial Differential Equations》2021,37(1):341-359
In this paper, a new computational scheme based on operational matrices (OMs) of two‐dimensional wavelets is proposed for the solution of variable‐order (VO) fractional partial integro‐differential equations (PIDEs). To accomplish this method, first OMs of integration and VO fractional derivative (FD) have been derived using two‐dimensional Legendre wavelets. By implementing two‐dimensional wavelets approximations and the OMs of integration and variable‐order fractional derivative (VO‐FD) along with collocation points, the VO fractional partial PIDEs are reduced into the system of algebraic equations. In addition to this, some useful theorems are discussed to establish the convergence analysis and error estimate of the proposed numerical technique. Furthermore, computational efficiency and applicability are examined through some illustrative examples. 相似文献
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We investigate the global existence and scattering for the cubic fourth‐order Schrödinger equation in a low regularity space with . We provide an alternative approach to obtain a new interaction Morawetz estimate which extends the range of the dimension of the interaction Morawetz estimate in Pausader 29 . We utilize the interaction Morawetz estimates and the I‐method to prove the global well‐posed and scattering result. 相似文献
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Xiaopeng Zhao Min Zhang Changchun Liu 《Mathematical Methods in the Applied Sciences》2013,36(2):169-181
This paper is concerned with a fourth‐order parabolic equation in one spatial dimension. On the basis of Leray–Schauder's fixed point theorem, we prove the existence and uniqueness of global weak solutions. Moreover, we also consider the regularity of solution and the existence of global attractor. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献