共查询到20条相似文献,搜索用时 15 毫秒
1.
We consider a splitting finite-difference scheme for an initial-boundary value problem for a two-dimensional nonlinear evolutionary
equation. The problem is split into nonlinear and linear parts. The linear part is also split into locally one-dimensional
equations. We prove the convergence and stability of the scheme in L
2 and C norms.
Printed in Lietuvos Matematikos Rinkinys, Vol. 45, No. 3, pp. 413–434, July–September, 2005. 相似文献
2.
Aurélien Deya 《Applied Mathematics and Optimization》2012,65(2):253-292
This paper is devoted to the study of numerical approximation schemes for a class of parabolic equations on (0,1) perturbed
by a non-linear rough signal. It is the continuation of Deya (Electron. J. Probab. 16:1489–1518, 2011) and Deya et al. (Probab. Theory Relat. Fields, to appear), where the existence and uniqueness of a solution has been established.
The approach combines rough paths methods with standard considerations on discretizing stochastic PDEs. The results apply
to a geometric 2-rough path, which covers the case of the multidimensional fractional Brownian motion with Hurst index H>1/3. 相似文献
3.
Differential Equations - For evolution problems, the approximate solution on the upper time level is often obtained from a number of simpler problems. Standard splitting schemes use an additive... 相似文献
4.
It is a very common practice to use semi-implicit schemes in various computations, which treat selected linear terms implicitly and the nonlinear terms explicitly. For phase-field equations, the principal elliptic operator is treated implicitly to reduce the associated stability constraints while the nonlinear terms are still treated explicitly to avoid the expensive process of solving nonlinear equations at each time step. However, very few recent numerical analysis is relevant to semi-implicit schemes, while "stabilized" schemes have become very popular. In this work, we will consider semi-implicit schemes for the Allen-Cahn equation with $general$ $potential$ function. It will be demonstrated that the maximum principle is valid and the energy stability also holds for the numerical solutions. This paper extends the result of Tang & Yang (J. Comput. Math., 34(5) (2016), pp. 471-481), which studies the semi-implicit scheme for the Allen-Cahn equation with $polynomial$ $potentials$. 相似文献
5.
Computational Mathematics and Mathematical Physics - Schemes of the Samarskii alternating triangular method are based on splitting the problem operator into two operators that are conjugate to each... 相似文献
6.
Kerli Orav-Puurand 《Numerical Functional Analysis & Optimization》2013,34(3-4):352-370
In a weakly singular integral equation of the second kind, we perform a smoothing change of variables and solve the resulting equation either by the collocation or by the product integration method based on a “central part” interpolation by polynomials on the uniform grid. Optimal convergence order of both methods is established. The latter method is hopeful due to especially simple and cheap assembling of the algebraic system of equations. 相似文献
7.
Stochastic evolutional equations with monotone operators are considered in Banach spaces. Explicit and implicit numerical schemes are presented. The convergence of the approximations to the solution of the equations is proved.
Mathematics Subject Classifications (2000) Primary: 60H15; Secondary: 65M60.István Gyöngy: This paper was written while the first named author was visiting the University of Paris X. The research of this author is partially supported by EU Network HARP.Annie Millet: The research of the second named author is partially supported by the research project BMF2003-01345. 相似文献
8.
熵相容格式相比于一般的熵稳定格式进一步控制了激波处的熵增量,一维情况下能有效消除膨胀激波及间断处的伪振荡等现象.对于Euler方程,可以通过对特征变量进行WENO重构以获得高阶熵相容格式的数值粘性项,然后与高阶熵守恒格式结合得到高精度熵相容格式,在WENO重构过程中的权重关于特征变量是非线性的,这导致了大量的向量内积运算.通过用压强和熵代替特征变量来计算权重,可以显著减少重构的计算量,并且数值算例表明这种权重的计算方式能很好地保持数值格式的高阶精度和基本无振荡的效果. 相似文献
9.
Ronald E. Mickens 《Journal of Difference Equations and Applications》2013,19(9):823-847
This paper gives an introduction to nonstandard finite difference methods useful for the construction of discrete models of differential equations when numerical solutions are required. While the general rules for such schemes are not precisely known at the present time, several important criterion have been found. We provide an explanation of their significance and apply them to several model ordinary and partial differential equations. The paper ends with a discussion of several outstanding problems in this area and other related issues. 相似文献
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Some new sixth-order compact finite difference schemes for Poisson/Helmholtz equations on rectangular domains in both two- and three-dimensions are
developed and analyzed. Different from a few sixth-order compact finite difference
schemes in the literature, the finite difference and weight coefficients of the new
methods have analytic simple expressions. One of the new ideas is to use a weighted
combination of the source term at staggered grid points which is important for grid
points near the boundary and avoids partial derivatives of the source term. Furthermore, the new compact schemes are exact for 2D and 3D Poisson equations if the
solution is a polynomial less than or equal to 6. The coefficient matrices of the new
schemes are $M$-matrices for Helmholtz equations with wave number $K≤0,$ which
guarantee the discrete maximum principle and lead to the convergence of the new
sixth-order compact schemes. Numerical examples in both 2D and 3D are presented
to verify the effectiveness of the proposed schemes. 相似文献
13.
Qing-Min Yang 《计算数学(英文版)》1992,10(1):21-28
This paper provides a new kind of three-layer explicit schemes for solving the operator equation. It has good stability, and suits particularly the semidiscrete problems arising from solving multi-dimensional parabolic-type equations by the finite element method. The amount of its computation time is far less than that of various economical schemes of the difference method. If the accuracy of the nonstandard finite element schemes (2.7) is not enough, it can be improved using extrapolations. 相似文献
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Differential Equations - For abstract nonlinear difference schemes with operators acting in finite-dimensional Banach spaces, a stability criterion is stated and proved; namely, for a consistent... 相似文献
16.
E. R. Jakobsen 《BIT Numerical Mathematics》2004,44(2):269-285
In this paper we provide estimates of the rates of convergence of monotone approximation schemes for non-convex equations in one space-dimension. The equations under consideration are the degenerate elliptic Isaacs equations with x-depending coefficients, and the results applies in particular to certain finite difference methods and control schemes based on the dynamic programming principle. Recently, Krylov, Barles, and Jakobsen obtained similar estimates for convex Hamilton–Jacobi–Bellman equations in arbitrary space-dimensions. Our results are only valid in one space-dimension, but they are the first results of this type for non-convex second-order equations. 相似文献
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We construct new HLL-type moving-water equilibria preserving upwind schemes for the one-dimensional Saint-Venant system of shallow water equations with nonflat bottom topography. The designed first-and secondorder schemes are tested on a number of numerical examples, in which we verify the well-balanced property as well as the ability of the proposed schemes to accurately capture small perturbations of moving-water steady states. 相似文献