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1.
In this paper,we present the semi-implicit Euler(SIE)numerical solution for stochastic pantograph equations with jumps and prove that the SIE approximation solution converges to the exact solution in the mean-square sense under the Local Lipschitz condition. 相似文献
2.
Anita T.?LaytonEmail author Michael L.?MinionEmail author 《BIT Numerical Mathematics》2005,45(2):341-373
This paper concerns a class of deferred correction methods recently developed for initial value ordinary differential equations;
such methods are based on a Picard integral form of the correction equation. These methods divide a given timestep [tn,tn+1] into substeps, and use function values computed at these substeps to approximate the Picard integral by means of a numerical
quadrature. The main purpose of this paper is to present a detailed analysis of the implications of the location of quadrature
nodes on the accuracy and stability of the overall method. Comparisons between Gauss-Legendre, Gauss-Lobatto, Gauss-Radau,
and uniformly spaced points are presented. Also, for a given set of quadrature nodes, quadrature rules may be formulated that
include or exclude function values computed at the left-hand endpoint tn. Quadrature rules that do not depend on the left-hand endpoint (which are referred to as right-hand quadrature rules) are
shown to lead to L(α)-stable implicit methods with α≈π/2. The semi-implicit analog of this property is also discussed. Numerical results suggest
that the use of uniform quadrature nodes, as opposed to nodes based on Gaussian quadratures, does not significantly affect
the stability or accuracy of these methods for orders less than ten. In contrast, a study of the reduction of order for stiff
equations shows that when uniform quadrature nodes are used in conjunction with a right-hand quadrature rule, the form and
extent of order-reduction changes considerably. Specifically, a reduction of order to
is observed for uniform nodes as opposed to
for non-uniform nodes, where Δt denotes the time step and ε a stiffness parameter such that ε→0 corresponds to the problem becoming increasingly stiff.
AMS subject classification (2000) 65B05 相似文献
3.
本文将移动粒子半隐式法(MPS)的基本算法由二维扩展至三维。将圆柱坐标系引入到初场粒子的布置中,避免了在笛卡儿坐标系下处理不规则形状(如斜边或曲边)问题时粒子初场布置困难和精确度较低的问题,改善了对计算边界条件表达的精确性。引入移动边界模型,对直叶片搅拌器的内部流动进行了三维数值模拟。还提出了一种新的初始粒子布置简易方法,明显简化粒子初始布置时的复杂程度,提高了对三维复杂几何形状问题的可操作性。 相似文献
4.
T-stability of the semi-implicit Euler method for delay differential equations with multiplicative noise 总被引:1,自引:0,他引:1
Wanrong Cao 《Applied mathematics and computation》2010,216(3):999-1006
The paper deals with the T-stability of the semi-implicit Euler method for delay differential equations with multiplicative noise. A difference equation is obtained by applying the numerical method to a linear test equation, in which the Wiener increment is approximated by a discrete random variable with two-point distribution. The conditions under which the method is T-stable are considered and the numerical experiments are given. 相似文献
5.
A. Chalabi. 《Mathematics of Computation》1999,68(227):955-970
We focus in this study on the convergence of a class of relaxation numerical schemes for hyperbolic scalar conservation laws including stiff source terms. Following Jin and Xin, we use as approximation of the scalar conservation law, a semi-linear hyperbolic system with a second stiff source term. This allows us to avoid the use of a Riemann solver in the construction of the numerical schemes. The convergence of the approximate solution toward a weak solution is established in the cases of first and second order accurate MUSCL relaxed methods.
6.
本文提出一类基于一维热传导方程数值求解的增量未知元方法加权半隐格式,并由此给出分析稳定性和整体截断误差的新方法.我们引入源于Laplace算子的两组基底,使得放大矩阵易于分析;我们利用IU性质和矩阵运算技巧,严格证明了所述加权格式的稳定性充分条件和全局误差估计,这些结果本质上优于1/4≤θ≤3/4条件下的常见情形.所得结论为恢复初始误差带来可能,为选择最优加权半隐格式提供了理论依据. 相似文献
7.
Tiangang Zhang Seiichi Koshizuka Kohei Murotani Kazuya Shibata Eiji Ishii Masanori Ishikawa 《International Journal of Computational Fluid Dynamics》2016,30(2):155-175
The boundary conditions represented by polygons in moving particle semi-implicit (MPS) method (Koshizuka and Oka, Nuclear Science and Engineering, 1996) have been widely used in the industry simulations since it can simply simulate complex geometry with high efficiency. However, the inaccurate particle number density near non-planar wall boundaries dramatically affects the accuracy of simulations. In this paper, we propose an initial boundary particle arrangement technique coupled with the wall weight function method (Zhang et al. Transaction of JSCES, 2015) to improve the particle number density near slopes and curved surfaces with boundary conditions represented by polygons in three dimensions. Two uniform grids are utilized in the proposed technique. The grid points in the first uniform grid are used to construct boundary particles, and the second uniform grid stores the same information as in the work by Zhang et al. The wall weight functions of the grid points in the second uniform grid are calculated by newly constructed boundary particles. The wall weight functions of the fluid particles are interpolated from the values stored on the grid points in the second uniform grid. Because boundary particles are located on the polygons, complex geometries can be accurately represented. The proposed method can dramatically improve the particle number density and maintain the high efficiency. The performance of the previously proposed wall weight function (Zhang et al.) with the boundary particle arrangement technique is verified in comparison with the wall weight function without boundary particle arrangement by investigating two example geometries. The simulations of a water tank with a wedge and a complex geometry show the general applicability of the boundary particle arrangement technique to complex geometries and demonstrate its improvement of the wall weight function near the slopes and curved surfaces. 相似文献
8.
In this note a simple characterization of 'strong' A-acceptability for a rational function is given. This fact meets applications in stability theory for Runge–Kutta or semi-implicit methods. In particular, strongly A-stable methods give (long time) stable integrations on autonomous differential systems possessing a semi-stable equilibrium. 相似文献
9.
Vincenzo Casulli 《国际流体数值方法杂志》2019,90(3):140-155
Free-surface flows in rivers, estuaries, and coastal areas are strongly dominated by the geometrical details of the study area. Nowadays, accurate bathymetric data are easily available on raster-based digital elevation models with an impressive spatial resolution. These data are often accessible as large two-dimensional arrays containing several millions of pixel values. Recent numerical methods are very efficient and rather accurate but far from being able to solve the governing differential equations on a computational grid with such a fine spatial resolution. In the present investigation, the unaltered pixel values from a digital elevation model are clustered to form subgrids of a coarser computational grid. Artificial cross-flow between disconnected areas is inhibited by introducing cell clones and edge clones. Each clone consists of directly connected pixels. It is shown how the resulting computational grid is able to resolve geometrical details of complex study areas to pixel resolution and for any grid size. As an example, the performance of the proposed algorithm is tested to simulate a typical tidal flow in the San Francisco Bay and the Sacramento-San Joaquin Delta area by using an extreme subgrid resolution given by a digital elevation model containing 196 000 000 pixels with 10 m pixel size. 相似文献
10.
In this paper, we present an efficient semi-implicit scheme for the solution of the Reynolds-averaged Navier-Stokes equations for the simulation of hydrostatic and nonhydrostatic free surface flow problems. A staggered unstructured mesh composed by Voronoi polygons is used to pave the horizontal domain, whereas parallel layers are adopted along the vertical direction. Pressure, velocity, and vertical viscosity terms are taken implicitly, whereas the nonlinear convective terms as well as the horizontal viscous terms are discretized explicitly by using a semi-Lagrangian approach, which requires an interpolation of the three-dimensional velocity field to integrate the flow trajectories backward in time. To this purpose, a high-order reconstruction technique is proposed, which is based on a constrained least squares operator that guarantees a globally and pointwise divergence-free velocity field. A comparison with an analogous reconstruction, which is not divergence-free preserving, is also presented to give evidence of the new strategy. This allows the continuity equation to be satisfied up to machine precision even for high-order spatial discretizations. The reconstructed velocity field is then used for evaluating high-order terms of a Taylor method that is here adopted as ODE integrator for the flow trajectories. The proposed semi-implicit scheme is validated against a set of academic test problems, and proof of convergence up to fourth-order of accuracy in space is shown. 相似文献