共查询到20条相似文献,搜索用时 15 毫秒
1.
S.H. Momeni‐Masuleh A. Malek 《Numerical Methods for Partial Differential Equations》2007,23(5):1139-1148
This research aims to develop a time‐dependent pseudospectral‐finite difference scheme for solving a 3D dual‐phase‐lagging heat transport equation in a submicroscale thin film. The scheme uses periodic pseudospectral discretization in space and a fully second‐order finite difference discretization in time. The three consecutive time steps model is then solved explicitly, by using a preconditioned conjugate gradient method. The scheme is illustrated by an example which is used to investigate the heat transfer in a gold submicroscale thin film. Comparisons are made with available literature. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007 相似文献
2.
Alaeddin Malek Sayed Hodjatollah Momeni-Masuleh 《Journal of Computational and Applied Mathematics》2008,217(1):137-147
Three-dimensional time-dependent initial-boundary value problems of a novel microscopic heat equation are solved by the mixed collocation–finite difference method in and on the boundaries of a particle when the thickness is much smaller than both the length and width. The collocation method on fixed grid size is used to approximate the space operator, whereas the finite difference scheme is used for time discretization. This new mixed method is applied to a novel heat problem in a particle, in order to compute the temperature distribution in and on the particle's surface. The second derivatives of the basis functions for the spectral approximation are derived. Direct substitution of derivatives in the model transforms the differential equation into a linear system of equations that is solved by the specific preconditioned conjugate gradient method. The high-order accuracy and resolution achieved by the proposed method allows one to obtain engineering-accuracy solution on coarse meshes. The consistency, stability and convergence analysis are provided and numerical results are presented. 相似文献
3.
Yuehong Qian Hudong Chen Raoyang Zhang Shiyi Chen 《Communications in Nonlinear Science & Numerical Simulation》2000,5(4):151-157
We propose and investigate a new simple fourth order finite difference scheme for the heat equation. Numerical simulations do confirm theoretical analysis of accuracy and stability condition. 相似文献
4.
Thanh Tran Thanh‐Binh Duong 《Numerical Methods for Partial Differential Equations》2005,21(3):521-535
A posteriori error estimates for semidiscrete finite element methods for a nonlinear Sobolev equation are considered. The error estimates are obtained by solving local nonlinear or linear pseudo‐parabolic equations for corrections to the solution on each element. The ratios of these estimates and the true errors are proved to converge to 1, implying that the estimates can be used as indicators in adaptive schemes for the problem. Numerical results underline our theoretical results. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005 相似文献
5.
Heat transport at the microscale is of vital importance in microtechnology applications. In this study, we develop a finite difference scheme of the Crank‐Nicholson type by introducing an intermediate function for the heat transport equation at the microscale. It is shown by the discrete energy method that the scheme is unconditionally stable. Numerical results show that the solution is accurate. © 1999 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 15: 697–708, 1999 相似文献
6.
In this paper, a class of finite difference method for solving two-sided space-fractional wave equation is considered. The stability and consistency of the method are discussed by means of Gerschgorin theorem and using the stability matrix analysis. Numerical solutions of some wave fractional partial differential equation models are presented. The results obtained are compared to exact solutions. 相似文献
7.
A compact finite difference scheme is developed to the three-dimensional microscale heat transport equation. This new scheme is fourth order in space and second order in time. It is proved to be unconditionally stable with respect to initial values. Numerical results are provided for comparison testing purpose. 相似文献
8.
For the multidimensional heat equation in a parallelepiped, optimal error estimates inL
2(Q) are derived. The error is of the order of +¦h¦2 for any right-hand sidef L
2(Q) and any initial function
; for appropriate classes of less regularf andu
0, the error is of the order of ((+¦h¦2
), 1/2<1.Translated fromMatematicheskie Zametki, Vol. 60, No. 2, pp. 185–197, August, 1996. 相似文献
9.
《Applied Mathematical Modelling》2014,38(15-16):3802-3821
In this paper, our aim is to study the high order finite difference method for the reaction and anomalous-diffusion equation. According to the equivalence of the Riemann–Liouville and Grünwald–Letnikov derivatives under the suitable smooth condition, a second-order difference approximation for the Riemann–Liouville fractional derivative is derived. A fourth-order compact difference approximation for second-order derivative in spatial is used. We analyze the solvability, conditional stability and convergence of the proposed scheme by using the Fourier method. Then we obtain that the convergence order is , where τ is the temporal step length and h is the spatial step length. Finally, numerical experiments are presented to show that the numerical results are in good agreement with the theoretical analysis. 相似文献
10.
In this article, we study a system of nonlinear parabolic partial differential equations arising from the heat and moisture transport through textile materials with phase change. A splitting finite difference method with semi‐implicit Euler scheme in time direction is proposed for solving the system of equations. We prove the existence and uniqueness of a classical positive solution to the parabolic system as well as the existence and uniqueness of a positive solution to the splitting finite difference system. We provide optimal error estimates for the splitting finite difference system under the condition that the mesh size and time step size are smaller than a positive constant which solely depends upon the physical parameters involved. Numerical results are presented to confirm our theoretical analysis. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2013 相似文献
11.
Numerical study using explicit multistep Galerkin finite element method for the MRLW equation 下载免费PDF全文
Liquan Mei Yali Gao Zhangxin Chen 《Numerical Methods for Partial Differential Equations》2015,31(6):1875-1889
In this article, an explicit multistep Galerkin finite element method for the modified regularized long wave equation is studied. The discretization of this equation in space is by linear finite elements, and the time discretization is based on explicit multistep schemes. Stability analysis and error estimates of our numerical scheme are derived. Numerical experiments indicate the validation of the scheme by L2– and L∞– error norms and three invariants of motion.4 © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1875–1889, 2015 相似文献
12.
In this paper, we present fourth-order finite difference method for solving nonlinear one-dimensional Burgers’ equation. This method is unconditionally stable. The convergence analysis of the present method is studied and an upper bound for the error is derived. Numerical comparisons are made with most of the existing numerical methods for solving this equation. 相似文献
13.
Zhiyue Zhang Dingwen Deng 《Numerical Methods for Partial Differential Equations》2007,23(6):1530-1559
A modified backward difference time discretization is presented for Galerkin approximations for nonlinear hyperbolic equation in two space variables. This procedure uses a local approximation of the coefficients based on patches of finite elements with these procedures, a multidimensional problem can be solved as a series of one‐dimensional problems. Optimal order H01 and L2 error estimates are derived. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007 相似文献
14.
Pavel Trojovský 《Journal of Difference Equations and Applications》2017,23(10):1737-1746
This paper is devoted to a generalization of some previous results, as we completely solve a linear homogeneous difference equation of the second order with an exponential coefficient. 相似文献
15.
LiHong WeiXiaoxi 《高校应用数学学报(英文版)》2005,20(1):97-104
A space-time finite element method,discontinuous in time but continuous in space, is studied to solve the nonlinear forward-backward heat equation. A linearized technique is introduced in order to obtain the error estimates of the approximate solutions. And the numerical simulations are given. 相似文献
16.
An implicit unconditional stable difference scheme is presented for a kind of linear space–time fractional convection–diffusion equation. The equation is obtained from the classical integer order convection–diffusion equations with fractional order derivatives for both space and time. First-order consistency, unconditional stability, and first-order convergence of the method are proven using a novel shifted version of the classical Grünwald finite difference approximation for the fractional derivatives. A numerical example with known exact solution is also presented, and the behavior of the error is examined to verify the order of convergence. 相似文献
17.
《Numerical Methods for Partial Differential Equations》2018,34(6):2024-2039
A second–order exponential time differencing scheme using the method of lines is developed in this article for the numerical solution of the Burgers and the modified Burgers equations. For each case, the resulting nonlinear system is solved explicitly using a modified predictor‐corrector method. The efficiency of the method introduced is tested by comparing experimental results with others selected from the available literature. 相似文献
18.
Zhiyue Zhang 《Numerical Methods for Partial Differential Equations》2004,20(6):855-863
Heat transport at the microscale is of vital importance in microtechnology applications. In this article, we proposed a new ADI difference scheme of the Crank‐Nicholson type for heat transport equation at the microscale. It is shown that the scheme is second order accurate in time and in space in the H1 norm. Numerical result implies that the theoretical analysis is correct and the scheme is effective. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2004 相似文献
19.
Murat Sari Gürhan Gürarslan İdris Dağ 《Numerical Methods for Partial Differential Equations》2010,26(1):125-134
In this article, numerical solutions of the generalized Burgers–Fisher equation are obtained using a compact finite difference method with minimal computational effort. To verify this, a combination of a sixth‐order compact finite difference scheme in space and a low‐storage third‐order total variation diminishing Runge–Kutta scheme in time have been used. The computed results with the use of this technique have been compared with the exact solution to show the accuracy of it. The approximate solutions to the equation have been computed without transforming the equation and without using linearization. Comparisons indicate that there is a very good agreement between the numerical solutions and the exact solutions in terms of accuracy. The present method is seen to be a very good alternative to some existing techniques for realistic problems. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010 相似文献
20.
构造了五维热传导方程的一族两层显格式,证明了当截断误差阶为O(τ+h2)时,其稳定性条件为网比r=hτ2≤21,优于同类的其它显格式,当截断误差阶为O(τ2+h2)时,可以得到一个简洁而实用的二阶精度的两层显格式. 相似文献