共查询到20条相似文献,搜索用时 31 毫秒
1.
In this paper a numerical technique is proposed for solving the time fractional diffusion-wave equation. We obtain a time discrete scheme based on finite difference formula. Then, we prove that the time discrete scheme is unconditionally stable and convergent using the energy method and the convergence order of the time discrete scheme is \(\mathcal {O}(\tau ^{3-\alpha })\). Firstly, we change the main problem based on Dirichlet boundary condition to a new problem based on Robin boundary condition and then, we consider a semi-discrete scheme with Robin boundary condition and show when \(\beta \rightarrow +\infty \) solution of the main semi-discrete problem with Dirichlet boundary condition is convergent to the solution of the new semi-discrete problem with Robin boundary condition. We consider the new semi-discrete problem with Robin boundary condition and use the meshless Galerkin method to approximate the spatial derivatives. Finally, we obtain an error bound for the new problem. We prove that convergence order of the numerical scheme based on Galekin meshless is \(\mathcal {O}(h)\). In the considered method the appeared integrals are approximated using Gauss Legendre quadrature formula. The main aim of the current paper is to obtain an error estimate for the meshless Galerkin method based on the radial basis functions. Numerical examples confirm the efficiency and accuracy of the proposed scheme. 相似文献
2.
Non-oscillatory schemes are widely used in numerical approximations of nonlinear conservation laws. The Nessyahu–Tadmor (NT) scheme is an example of a second order scheme that is both robust and simple. In this paper, we prove a new stability property of the NT scheme based on the standard minmod reconstruction in the case of a scalar strictly convex conservation law. This property is similar to the One-sided Lipschitz condition for first order schemes. Using this new stability, we derive the convergence of the NT scheme to the exact entropy solution without imposing any nonhomogeneous limitations on the method. We also derive an error estimate for monotone initial data. 相似文献
3.
基于新光滑因子的WENO5格式 总被引:1,自引:0,他引:1
针对WENO格式的构造,本文给出了一个WENO为5阶的充分条件,降低了Henrick等人提出的充分条件对于权因子的精度要求.另外,对于Jiang和Shu提出的WENO5中的光滑因子中两项的系数做出了调整,并结合Borges等人的方法得到了新的WENO权因子计算方法.从数值试验的结果可以看出,新的WENO格式对于连续波形... 相似文献
4.
In this paper, we propose a stable high accurate hybrid scheme based on nonstandard Runge–Kutta (NRK) and modified weighted essentially non-oscillatory (MWENO) techniques for nonlinear degenerate parabolic partial differential equations. The necessary stability condition for the combination of a Runge–Kutta and MWENO scheme is given. The stability condition provides a renormalization function such that mixture of explicit NRK and MWENO scheme is unconditionally stable. Novel scheme recovers the sixth order convergent at points of inflection and prevents the appearance of spurious solutions close to discontinuities. The good performance of this scheme is illustrated through five examples. Numerical results are presented. 相似文献
5.
In this work, we generalize the current theory of strong convergence rates for the backward Euler–Maruyama scheme for highly non-linear stochastic differential equations, which appear in both mathematical finance and bio-mathematics. More precisely, we show that under a dissipative condition on the drift coefficient and super-linear growth condition on the diffusion coefficient the BEM scheme converges with strong order of a half. This type of convergence gives theoretical foundations for efficient variance reduction techniques for Monte Carlo simulations. We support our theoretical results with relevant examples, such as stochastic population models and stochastic volatility models. 相似文献
6.
Andreas Meister 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2003,54(6):1010-1049
In [43] a finite volume method for
reliable simulations of inviscid fluid flows at high as well as
low Mach numbers based on a preconditioning technique proposed by
Guillard and Viozat [14] is presented. In this paper
we describe an extension of the numerical scheme for computing
solutions of the Euler and Navier-Stokes equations. At first we
show the high resolution properties, accuracy and robustness of
the finite volume scheme in the context of a wide range of
complicated transonic and supersonic test cases whereby both
inviscid and viscous flow fields are considered. Thereafter, the
validity of the method in the low Mach number regime is proven by
means of an asymptotic analysis as well as numerical simulations.
Whereas in [43] the asymptotic analysis of the
scheme is focused on the behaviour of the continuous and discrete
pressure distribution for inviscid low speed simulations we prove
both the physical sensible discrete pressure field for viscous low
Mach number flows and the divergence free condition of the
discrete velocity field in the limit of a vanishing Mach number
with respect to the simulation of inviscid fluid flow. 相似文献
7.
Andreas Meister 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2003,41(5):1010-1049
In [43] a finite volume method for
reliable simulations of inviscid fluid flows at high as well as
low Mach numbers based on a preconditioning technique proposed by
Guillard and Viozat [14] is presented. In this paper
we describe an extension of the numerical scheme for computing
solutions of the Euler and Navier-Stokes equations. At first we
show the high resolution properties, accuracy and robustness of
the finite volume scheme in the context of a wide range of
complicated transonic and supersonic test cases whereby both
inviscid and viscous flow fields are considered. Thereafter, the
validity of the method in the low Mach number regime is proven by
means of an asymptotic analysis as well as numerical simulations.
Whereas in [43] the asymptotic analysis of the
scheme is focused on the behaviour of the continuous and discrete
pressure distribution for inviscid low speed simulations we prove
both the physical sensible discrete pressure field for viscous low
Mach number flows and the divergence free condition of the
discrete velocity field in the limit of a vanishing Mach number
with respect to the simulation of inviscid fluid flow. 相似文献
8.
Mikael Barboteu Mircea Sofonea 《Journal of Mathematical Analysis and Applications》2009,358(1):110-2991
We consider a mathematical model which describes the quasistatic process of contact between a piezoelectric body and an electrically conductive support, the so-called foundation. We model the material's behavior with a nonlinear electro-viscoelastic constitutive law; the contact is frictionless and is described with the Signorini condition and a regularized electrical conductivity condition. We derive a variational formulation for the problem and then we prove the existence of a unique weak solution to the model. The proof is based on arguments of nonlinear equations with multivalued maximal monotone operators and fixed point. Then we introduce a fully discrete scheme, based on the finite element method to approximate the spatial variable and the backward Euler scheme to discretize the time derivatives. We treat the unilateral contact conditions by using an augmented Lagrangian approach. We implement this scheme in a numerical code then we present numerical simulations in the study of two-dimensional test problems, together with various comments and interpretations. 相似文献
9.
In this article, a decoupling scheme based on two‐grid finite element for the mixed Stokes‐Darcy problem with the Beavers‐Joseph interface condition is proposed and investigated. With a restriction of a physical parameter α, we derive the numerical stability and error estimates for the scheme. Numerical experiments indicate that such two‐grid based decoupling finite element schemes are feasible and efficient. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 1066–1082, 2014 相似文献
10.
Choon Ki Ahn 《Journal of Optimization Theory and Applications》2014,160(2):659-678
In this paper, we present a new receding horizon neural robust control scheme for a class of nonlinear systems based on the linear differential inclusion (LDI) representation of neural networks. First, we propose a linear matrix inequality (LMI) condition on the terminal weighting matrix for a receding horizon neural robust control scheme. This condition guarantees the nonincreasing monotonicity of the saddle point value of the finite horizon dynamic game. We then propose a receding horizon neural robust control scheme for nonlinear systems, which ensures the infinite horizon robust performance and the internal stability of closed-loop systems. Since the proposed control scheme can effectively deal with input and state constraints in an optimization problem, it does not cause the instability problem or give the poor performance associated with the existing neural robust control schemes. 相似文献
11.
In this paper, two new energy-conserved splitting methods (EC-S-FDTDI and EC-S-FDTDII) for Maxwell’s equations in two dimensions
are proposed. Both algorithms are energy-conserved, unconditionally stable and can be computed efficiently. The convergence
results are analyzed based on the energy method, which show that the EC-S-FDTDI scheme is of first order in time and of second
order in space, and the EC-S-FDTDII scheme is of second order both in time and space. We also obtain two identities of the
discrete divergence of electric fields for these two schemes. For the EC-S-FDTDII scheme, we prove that the discrete divergence
is of first order to approximate the exact divergence condition. Numerical dispersion analysis shows that these two schemes
are non-dissipative. Numerical experiments confirm well the theoretical analysis results. 相似文献
12.
Jun-yong Zhai Wen-ting Zha Shu-min Fei 《Communications in Nonlinear Science & Numerical Simulation》2013,18(11):3181-3189
This paper addresses the problem of semi-global finite-time decentralized output feedback control for large-scale systems with both higher-order and lower-order terms. A new design scheme is developed by coupling the finite-time output feedback stabilization method with the homogeneous domination approach. Specifically, we first design a homogeneous observer and an output feedback control law for each nominal subsystem without the nonlinearities. Then, based on the homogeneous domination approach, we relax the linear growth condition to a polynomial one and construct decentralized controllers to render the nonlinear system semi-globally finite-time stable. 相似文献
13.
In this note, we study the convergence of the Levenberg–Marquardt regularization scheme for nonlinear ill-posed problems.
We consider the case that the initial error satisfies a source condition. Our main result shows that if the regularization
parameter does not grow too fast (not faster than a geometric sequence), then the scheme converges with optimal convergence
rates. Our analysis is based on our recent work on the convergence of the exponential Euler regularization scheme (Hochbruck
et al. in Inverse Probl 25(7):075009, 2009). 相似文献
14.
Vector and Hermite subdivision schemes both act on vector data, but since the latter one interprets the vectors as function
values and consecutive derivatives they differ by the “renormalization” of the Hermite scheme in any step. In this paper we
give an algebraic factorization method in one and several variables to relate any Hermite subdivision scheme that satisfies
the so–called spectral condition to a vector subdivision scheme. These factorizations are natural extensions of the “zero
at π” condition known for the masks of refinable functions. Moreover, we show how this factorization can be used to investigate
different forms of convergence of the Hermite scheme and why the multivariate situation is conceptionally more intricate than
the univariate one. Finally, we give some examples of such factorizations. 相似文献
15.
针对 1 997年全国大学生数学建模竟赛 B题 ,对于换刀费用 e=0的情况 ,本文设计了一种异常简捷的切割厚度排序法来寻找最优切割方案 ,同时在数学上给出了严格的证明 .对于换刀费用 e≠ 0的情况 ,以 e=0时得到的最优切割方案为基础 ,先通过简单的调整原则寻找出限定不同换刀次数时各自的最优切割方案 ,再通过费用比较便可简捷地得到随 e值的大小而变化的最优切割方案 .本文构造的模型在求解时无须用计算机编程 ,只用手算即可简捷地得到答案 相似文献
16.
A new general scheme for Inexact Restoration methods for Nonlinear Programming is introduced. After computing an inexactly
restored point, the new iterate is determined in an approximate tangent affine subspace by means of a simple line search on
a penalty function. This differs from previous methods, in which the tangent phase needs both a line search based on the objective
function (or its Lagrangian) and a confirmation based on a penalty function or a filter decision scheme. Besides its simplicity
the new scheme enjoys some nice theoretical properties. In particular, a key condition for the inexact restoration step could
be weakened. To some extent this also enables the application of the new scheme to mathematical programs with complementarity
constraints. 相似文献
17.
《Studies in Applied Mathematics》2018,140(4):483-507
We propose an integrable discrete model of one‐dimensional soil water infiltration. This model is based on the continuum model by Broadbridge and White, which takes the form of nonlinear convection–diffusion equation with a nonlinear flux boundary condition at the surface. It is transformed to the Burgers equation with a time‐dependent flux term by the hodograph transformation. We construct a discrete model preserving the underlying integrability, which is formulated as the self‐adaptive moving mesh scheme. The discretization is based on linearizability of the Burgers equation to the linear diffusion equation, but the naïve discretization based on the Euler scheme which is often used in the theory of discrete integrable systems does not necessarily give a good numerical scheme. Taking desirable properties of a numerical scheme into account, we propose an alternative discrete model that produces solutions with similar accuracy to direct computation on the original nonlinear equation, but with clear benefits regarding computational cost. 相似文献
18.
19.
《Journal of Computational and Applied Mathematics》2012,236(4):565-574
In a recent paper, we investigated factorization properties of Hermite subdivision schemes by means of the so-called Taylor factorization. This decomposition is based on a spectral condition which is satisfied for example by all interpolatory Hermite schemes. Nevertheless, there exist examples of Hermite schemes, especially some based on cardinal splines, which fail the spectral condition. For these schemes (and others) we provide the concept of a generalized Taylor factorization and show how it can be used to obtain convergence criteria for the Hermite scheme by means of factorization and contractivity. 相似文献
20.
Jean-Louis Merrien 《Journal of Computational and Applied Mathematics》2011,236(4):565-574
In a recent paper, we investigated factorization properties of Hermite subdivision schemes by means of the so-called Taylor factorization. This decomposition is based on a spectral condition which is satisfied for example by all interpolatory Hermite schemes. Nevertheless, there exist examples of Hermite schemes, especially some based on cardinal splines, which fail the spectral condition. For these schemes (and others) we provide the concept of a generalized Taylor factorization and show how it can be used to obtain convergence criteria for the Hermite scheme by means of factorization and contractivity. 相似文献