共查询到20条相似文献,搜索用时 31 毫秒
1.
Xue-Cheng Tai 《Numerical Algorithms》1992,3(1):427-440
Extrapolation with a parallel splitting method is discussed. The parallel splitting method reduces a multidimensional problem into independent one-dimensional problems and can improve the convergence order of space variables to an order as high as the regularity of the solution permits. Therefore, in order to match the convergence order of the space variables, a high order method should also be used for the time integration. Second and third order extrapolation methods are used to improve the time convergence and it was found that the higher order extrapolation method can produce a more accurate solution than the lower order extrapolation method, but the convergence order of high order extrapolation may be less than the actual order of the extrapolation. We also try to show a fact that has not been studied in the literature, i.e. when the extrapolation is used, it may decrease the convergence of the space variables. The higher the order of the extrapolation method, the more it decreases the convergence of the space variables. The global extrapolation method also improves the parallel degree of the parallel splitting method. Numerical tests in the paper are done in a domain of a unit circle and a unit square.Supported by the Academy of Finland. 相似文献
2.
冀敏 《数学的实践与认识》2013,43(10)
现代控制增稳飞机是高达几十阶的复杂系统,将其降阶为特定形式的低阶等效系统才能与已有飞行品质规范进行比较,进而预测和评价飞机飞行品质.从时域角度出发,提出了一种高阶控制增稳系统等效拟配参数在线辨识方法.分析了时域等效系统拟配的基本方法,提出了等效系统实时在线拟配的系统框架思路,基于Tustin变换法推导了由高阶系统时域响应获取四阶等效系统参数的数学公式,应用最小二乘法在MATLAB中实现了算法编程,并用试飞数据验证了所提方法的可行性.计算结果表明,所提方法可以快速准确地实现高阶控制增稳系统的等效系统参数辨识. 相似文献
3.
A high‐order compact ADI method for solving three‐dimensional unsteady convection‐diffusion problems
Samir Karaa 《Numerical Methods for Partial Differential Equations》2006,22(4):983-993
We derive a high‐order compact alternating direction implicit (ADI) method for solving three‐dimentional unsteady convection‐diffusion problems. The method is fourth‐order in space and second‐order in time. It permits multiple uses of the one‐dimensional tridiagonal algorithm with a considerable saving in computing time and results in a very efficient solver. It is shown through a discrete Fourier analysis that the method is unconditionally stable in the diffusion case. Numerical experiments are conducted to test its high order and to compare it with the standard second‐order Douglas‐Gunn ADI method and the spatial fourth‐order compact scheme by Karaa. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006 相似文献
4.
The fourth order average vector field (AVF) method is applied to solve
the "Good" Boussinesq equation. The semi-discrete system of the "good" Boussinesq
equation obtained by the pseudo-spectral method in spatial variable, which is a
classical finite dimensional Hamiltonian system, is discretized by the fourth order
average vector field method. Thus, a new high order energy conservation scheme of
the "good" Boussinesq equation is obtained. Numerical experiments confirm that the
new high order scheme can preserve the discrete energy of the "good" Boussinesq
equation exactly and simulate evolution of different solitary waves well. 相似文献
5.
In this paper, a high order accurate spectral method is presented
for the space-fractional diffusion equations. Based on Fourier
spectral method in space and Chebyshev collocation method in time,
three high order accuracy schemes are proposed. The main advantages
of this method are that it yields a fully diagonal representation of
the fractional operator, with increased accuracy and efficiency
compared with low-order counterparts, and a completely
straightforward extension to high spatial dimensions. Some numerical
examples, including Allen-Cahn equation, are conducted to verify the
effectiveness of this method. 相似文献
6.
Akbar Mohebbi Mehdi Dehghan 《Numerical Methods for Partial Differential Equations》2008,24(5):1222-1235
In this article, we introduce a high‐order accurate method for solving one‐space dimensional linear hyperbolic equation. We apply a compact finite difference approximation of fourth order for discretizing spatial derivative of linear hyperbolic equation and collocation method for the time component. The main property of this method additional to its high‐order accuracy due to the fourth order discretization of spatial derivative, is its unconditionally stability. In this technique the solution is approximated by a polynomial at each grid point that its coefficients are determined by solving a linear system of equations. Numerical results show that the compact finite difference approximation of fourth order and collocation method produce a very efficient method for solving the one‐space‐dimensional linear hyperbolic equation. We compare the numerical results of this paper with numerical results of (Mohanty, 3 .© 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2008 相似文献
7.
Numerical differentiation is a classical ill-posed problem. In this paper, a wavelet regularization method for high order numerical derivatives is given and an order optimal Hölder-type stability estimate is also provided. Some numerical examples show that the method is very effective. 相似文献
8.
Mehdi Dehghan Akbar Mohebbi 《Numerical Methods for Partial Differential Equations》2009,25(1):232-243
In this article, we introduce a high‐order accurate method for solving the two dimensional linear hyperbolic equation. We apply a compact finite difference approximation of fourth order for discretizing spatial derivatives of linear hyperbolic equation and collocation method for the time component. The resulted method is unconditionally stable and solves the two‐dimensional linear hyperbolic equation with high accuracy. In this technique, the solution is approximated by a polynomial at each grid point that its coefficients are determined by solving a linear system of equations. Numerical results show that the compact finite difference approximation of fourth order and collocation method give a very efficient approach for solving the two dimensional linear hyperbolic equation. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009 相似文献
9.
Chunmei Xie & Minfu Feng 《计算数学(英文版)》2020,38(3):395-416
In this paper, we present a new stabilized finite element method for transient Navier-Stokes equations with high Reynolds number based on the projection of the velocity and
pressure. We use Taylor-Hood elements and the equal order elements in space and second
order difference in time to get the fully discrete scheme. The scheme is proven to possess the
absolute stability and the optimal error estimates. Numerical experiments show that our
method is effective for transient Navier-Stokes equations with high Reynolds number and
the results are in good agreement with the value of subgrid-scale eddy viscosity methods,
Petro-Galerkin finite element method and streamline diffusion method. 相似文献
10.
Pavel N. Ryabov Dmitry I. SinelshchikovMark B. Kochanov 《Applied mathematics and computation》2011,218(7):3965-3972
The application of the Kudryashov method for finding exact solutions of the high order nonlinear evolution equations is considered. Some classes of solitary wave solutions for the families of nonlinear evolution equations of fifth, sixth and seventh order are obtained. The efficiency of the Kudryashov method for finding exact solutions of the high order nonlinear evolution equations is demonstrated. 相似文献
11.
Numerical differentiation is a classical ill-posed problem. In this paper, we propose a wavelet-Galerkin method for high order numerical differentiation. By an appropriate choice of the regularization parameter an order optimal stability estimate of Hölder type is obtained. Some numerical examples show that the method is effective and stable. 相似文献
12.
13.
Xin Wen 《计算数学(英文版)》2011,29(3):305-323
In this paper we design and analyze a class of high order numerical methods to two dimensional Heaviside function integrals. Inspired by our high order numerical methods to two dimensional delta function integrals [19], the methods comprise approximating the mesh cell restrictions of the Heaviside function integral. In each mesh cell the two dimensional Heaviside function integral can be rewritten as a one dimensional ordinary integral with the integrand being a one dimensional Heaviside function integral which is smooth on several subsets of the integral interval. Thus the two dimensional Heaviside function integral is approximated by applying standard one dimensional high order numerical quadratures and high order numerical methods to one dimensional Heaviside function integrals. We establish error estimates for the method which show that the method can achieve any desired accuracy by assigning the corresponding accuracy to the sub-algorithms. Numerical examples are presented showing that the second- to fourth-order methods implemented in this paper achieve or exceed the expected accuracy. 相似文献
14.
Yongbin Ge Zhen F. Tian Jun Zhang 《Numerical Methods for Partial Differential Equations》2013,29(1):186-205
In this article, we develop an exponential high order compact alternating direction implicit (EHOC ADI) method for solving three dimensional (3D) unsteady convection–diffusion equations. The method, which requires only a regular seven‐point 3D stencil similar to that in the standard second‐order methods, is second order accurate in time and fourth‐order accurate in space and unconditionally stable. The resulting EHOC ADI scheme in each alternating direction implicit (ADI) solution step corresponding to a strictly diagonally dominant matrix equation can be solved by the application of the one‐dimensional tridiagonal Thomas algorithm with a considerable saving in computing time. Numerical experiments for three test problems are carried out to demonstrate the performance of the present method and to compare it with the classical Douglas–Gunn ADI method and the Karaa's high‐order compact ADI method. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2013 相似文献
15.
MA LiMin & WU ZongMin Shanghai Key Laboratory for Contemporary Applied Mathematics School of Mathematical Sciences Fudan University Shanghai China 《中国科学 数学(英文版)》2010,(4)
Numerical simulation of the high order derivatives based on the sampling data is an important and basic problem in numerical approximation,especially for solving the differential equations numerically.The classical method is the divided difference method.However,it has been shown strongly unstable in practice.Actually,it can only be used to simulate the lower order derivatives in applications.To simulate the high order derivatives,this paper suggests a new method using multiquadric quasi-interpolation.The s... 相似文献
16.
A high accuracy minimally invasive regularization technique for navier–stokes equations at high reynolds number 下载免费PDF全文
Mustafa Aggul Alexander Labovsky 《Numerical Methods for Partial Differential Equations》2017,33(3):814-839
A method is presented, that combines the defect and deferred correction approaches to approximate solutions of Navier–Stokes equations at high Reynolds number. The method is of high accuracy in both space and time, and it allows for the usage of legacy codes a frequent requirement in the simulation of turbulent flows in complex geometries. The two‐step method is considered here; to obtain a regularization that is second order accurate in space and time, the method computes a low‐order accurate, stable, and computationally inexpensive approximation (Backward Euler with artificial viscosity) twice. The results are readily extendable to the higher order accuracy cases by adding more correction steps. Both the theoretical results and the numerical tests provided demonstrate that the computed solution is stable and the accuracy in both space and time is improved after the correction step. We also perform a qualitative test to demonstrate that the method is capable of capturing qualitative features of a turbulent flow, even on a very coarse mesh. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 814–839, 2017 相似文献
17.
《Journal of the Egyptian Mathematical Society》2014,22(1):115-122
An efficient numerical method based on quintic nonpolynomial spline basis and high order finite difference approximations has been presented. The scheme deals with the space containing hyperbolic and polynomial functions as spline basis. With the help of spline functions we derive consistency conditions and high order discretizations of the differential equation with the significant first order derivative. The error analysis of the new method is discussed briefly. The new method is analyzed for its efficiency using the physical problems. The order and accuracy of the proposed method have been analyzed in terms of maximum errors and root mean square errors. 相似文献
18.
We consider high order finite difference methods for two-dimensional fractional differential equations with temporal Caputo and spatial Riemann-Liouville derivatives in this paper. We propose a scheme and show that it converges with second order in time and fourth order in space. The accuracy of our proposed method can be improved by Richardson extrapolation. Approximate solution is obtained by the generalized minimal residual (GMRES) method. A preconditioner is proposed to improve the efficiency for the implementation of the GMRES method. 相似文献
19.
J. R. Cash 《Numerische Mathematik》1982,40(3):329-337
Summary A widely used technique for improving the accuracy of solutions of initial value problems in ordinary differential equations is local extrapolation. It is well known, however, that when using methods appropriate for solving stiff systems of ODES, the stability of the method can be seriously degraded if local extrapolation is employed. This is due to the fact that performing local extrapolation on a low order method is equivalent to using a higher order formula and this high order formula may not be suitable for solving stiff systems. In the present paper a general approach is proposed whereby the correction term added on in the process of local extrapolation is in a sense a rational, rather than a polynomial, function. This approach allows high order formulae with bounded growth functions to be developed. As an example we derive anA-stable rational correction algorithm based on the trapezoidal rule. This new algorithm is found to be efficient when low accuracy is requested (say a relative accuracy of about 1%) and its performance is compared with that of the more familiar Richardson extrapolation method on a large set of stiff test problems. 相似文献
20.
Doklady Mathematics - A method is proposed for constructing combined shock-capturing finite-difference schemes that localize shock fronts with high accuracy and preserve the high order of... 相似文献