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1.
Xiaolin Zhou 《Numerical Methods for Partial Differential Equations》2004,20(2):193-198
This note presents a wavelets‐Galerkin scheme for the numerical solution of a Stokes problem by using the scaling function of a symmetric biorthogonal spline wavelets that can be modified to generate the divergence‐free wavelets. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 20: 193–198, 2004 相似文献
2.
Jérôme Droniou Robert Eymard 《Numerical Methods for Partial Differential Equations》2009,25(1):137-171
We present finite volume schemes for Stokes and Navier‐Stokes equations. These schemes are based on the mixed finite volume introduced in (Droniou and Eymard, Numer Math 105 (2006), 35‐71), and can be applied to any type of grid (without “orthogonality” assumptions as for classical finite volume methods) and in any space dimension. We present numerical results on some irregular grids, and we prove, for both Stokes and Navier‐Stokes equations, the convergence of the scheme toward a solution of the continuous problem. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009 相似文献
3.
Approximation of the unsteady Brinkman‐Forchheimer equations by the pressure stabilization method
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Mohammed Louaked Nour Seloula Saber Trabelsi 《Numerical Methods for Partial Differential Equations》2017,33(6):1949-1965
In this work, we propose and analyze the pressure stabilization method for the unsteady incompressible Brinkman‐Forchheimer equations. We present a time discretization scheme which can be used with any consistent finite element space approximation. Second‐order error estimate is proven. Some numerical results are also given.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1949–1965, 2017 相似文献
4.
《Numerical Methods for Partial Differential Equations》2006,22(2):506-506
The original article to which this erratum refers was published in Numerical Methods for Partial Differential Equations Numer Methods Partial Differential Eq(2006)22(1)180 相似文献
5.
《Numerical Methods for Partial Differential Equations》2007,23(1):246-246
It has come to the attention of the editors and publisher that an article published in Numerical Methods and Partial Differential Equations, Second‐order Galerkin‐Lagrange method for the Navier‐Stokes equations, by Mohamed Bensaada, Driss Esselaoui, and Pierre Saramito, Numer Methods Partial Differential Eq 21(6) (2005), 1099–1121, Numerical Methods for Partial Differential Equations Numer Methods Partial Differential Eq(2005)21(6)1099 included large portions that were copied from the following paper without proper citation: Convergence and nonlinear stability of the Lagrange‐Galerkin method for the Navier‐Stokes equations, Endre Suli, Numerische Mathematik, Vol. 53, No. 4, pp. 459–486 (July, 1988). We have retracted the paper and apologize to Dr. Suli. 相似文献
6.
R. J. Whitley T. V. Hromadka 《Numerical Methods for Partial Differential Equations》2001,17(4):332-335
The solution to any 2‐dimensional potential problem, with continuous data given on the boundary of a bounded domain with connected complement, can be approximated by sums Re Σ cn f(αn z + z0), where f is any preassigned non‐polynomial analytic function. © 2001 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 17:332–335, 2001 相似文献
7.
Zhi‐Zhong Sun 《Numerical Methods for Partial Differential Equations》2009,25(6):1320-1341
In this article, two recent proposed compact schemes for the heat conduction problem with Neumann boundary conditions are analyzed. The first difference scheme was proposed by Zhao, Dai, and Niu (Numer Methods Partial Differential Eq 23, (2007), 949–959). The unconditional stability and convergence are proved by the energy methods. The convergence order is O(τ2 + h2.5) in a discrete maximum norm. Numerical examples demonstrate that the convergence order of the scheme can not exceeds O(τ2 + h3). An improved compact scheme is presented, by which the approximate values at the boundary points can be obtained directly. The second scheme was given by Liao, Zhu, and Khaliq (Methods Partial Differential Eq 22, (2006), 600–616). The unconditional stability and convergence are also shown. By the way, it is reported how to avoid computing the values at the fictitious points. Some numerical examples are presented to show the theoretical results. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009 相似文献
8.
M.M. Rashidi D.D. Ganji S. Dinarvand 《Numerical Methods for Partial Differential Equations》2009,25(2):409-417
In this article, we apply the homotopy perturbation method (HPM) to obtain approximate analytical solutions of the generalized Burger and Burger‐Fisher (B–F) equations. Several numerical examples are given to illustrate the efficiency of the HPM. Comparison of the result obtained by the present method with exact solution reveals that the accuracy and fast convergence of the new method. It is predicted that the HPM can be found wide application in engineering problems. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009 相似文献
9.
C. V. Pao 《Numerical Methods for Partial Differential Equations》1998,14(3):339-351
In this article we use the monotone method for the computation of numerical solutions of a nonlinear reaction-diffusion-convection problem with time delay. Three monotone iteration processes for a suitably formulated finite-difference system of the problem are presented. It is shown that the sequence of iteration from each of these iterative schemes converges from either above or below to a unique solution of the finite-difference system without any monotone condition on the nonlinear reaction function. An analytical comparison result among the three processes of iterations is given. Also given is the application of the iterative schemes to some model problems in population dynamics, including numerical results of a model problem with known analytical solution. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 339–351, 1998 相似文献
10.
Numerical solution of linear and nonlinear partial differential equations using the peridynamic differential operator
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Erdogan Madenci Mehmet Dorduncu Atila Barut Michael Futch 《Numerical Methods for Partial Differential Equations》2017,33(5):1726-1753
This study presents numerical solutions to linear and nonlinear Partial Differential Equations (PDEs) by using the peridynamic differential operator. The solution process involves neither a derivative reduction process nor a special treatment to remove a jump discontinuity or a singularity. The peridynamic discretization can be both in time and space. The accuracy and robustness of this differential operator is demonstrated by considering challenging linear, nonlinear, and coupled PDEs subjected to Dirichlet and Neumann‐type boundary conditions. Their numerical solutions are achieved using either implicit or explicit methods. © 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1726–1753, 2017 相似文献
11.
Ahmet Yildirim Murat Erşen Berberler 《Numerical Methods for Partial Differential Equations》2010,26(5):1040-1053
In this article, we applied homotopy perturbation method to obtain the solution of the Korteweg‐de Vries Burgers (for short, KdVB) and Lax's seventh‐order KdV (for short, LsKdV) equations. The numerical results show that homotopy perturbation method can be readily implemented to this type of nonlinear equations and excellent accuracy. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010 相似文献
12.
Jae Ryong Kweon 《Numerical Methods for Partial Differential Equations》2004,20(3):412-431
A linearized compressible viscous Stokes system is considered. The a posteriori error estimates are defined and compared with the true error. They are shown to be globally upper and locally lower bounds for the true error of the finite element solution. Some numerical examples are given, showing an efficiency of the estimator. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 20: 412–431, 2004. 相似文献
13.
Mustafa Gülsu Mehmet Sezer 《Numerical Methods for Partial Differential Equations》2011,27(6):1628-1638
A numerical method based on the Taylor polynomials is introduced in this article for the approximate solution of the pantograph equations with constant and variable coefficients. Some numerical examples, which consist of the initial conditions, are given to show the properties of the method. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27:1628–1638, 2011 相似文献
14.
This article derives the weak estimate of the first type for pentahedral finite elements over uniform partitions of the domain for the Poisson equation. The estimate for the W1,1‐seminorm of the discrete derivative Green's function is also given. Using these two estimates, we obtain the pointwise supercloseness of derivatives of the pentahedral finite element approximation and the interpolant to the true solution. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010 相似文献
15.
In this research, the problem of solving the two‐dimensional parabolic equation subject to a given initial condition and nonlocal boundary specifications is considered. A technique based on the pseudospectral Legendre method is proposed for the numerical solution of the studied problem. Several examples are given and the numerical results are shown to demonstrate the efficiently of the newly proposed method. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006 相似文献
16.
Mi-Young Kim 《Numerical Methods for Partial Differential Equations》1998,14(3):317-337
A finite difference scheme along the characteristics is used to approximate the solution of an age-dependent s-i-s epidemic model. The global behavior of the discrete solution resulting from the algorithm is investigated. It is shown that a nontrivial discrete periodic solution is generated by a periodic force of infection. Sufficient (and explicit) threshold conditions for the existence and stability of a unique nontrivial periodic solution are given. Results from numerical experiments are presented. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 317–337, 1998 相似文献
17.
Polynomial preserving gradient recovery technique under anisotropic meshes is further studied for quadratic elements. The analysis is performed for highly anisotropic meshes where the aspect ratios of element sides are unbounded. When the mesh is adapted to the solution that has significant changes in one direction but very little, if any, in another direction, the recovered gradient can be superconvergent. The results further explain why recovery type error estimator is robust even under nonstandard and highly distorted meshes. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2011 相似文献
18.
N. Khiari T. Achouri M.L. Ben Mohamed K. Omrani 《Numerical Methods for Partial Differential Equations》2007,23(2):437-455
In this article, we analyze a Crank‐Nicolson‐type finite difference scheme for the nonlinear evolutionary Cahn‐Hilliard equation. We prove existence, uniqueness and convergence of the difference solution. An iterative algorithm for the difference scheme is given and its convergence is proved. A linearized difference scheme is presented, which is also second‐order convergent. Finally a new difference method possess a Lyapunov function is presented. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 23: 437–455, 2007 相似文献
19.
Mohamed Bensaada Driss Esselaoui Pierre Saramito 《Numerical Methods for Partial Differential Equations》2005,21(6):1099-1121
It has come to the attention of the editors and publisher that an article published in Numerical Methods and Partial Differential Equations, “Second‐order Galerkin‐Lagrange method for the Navier‐Stokes equations,” by Mohamed Bensaada, Driss Esselaoui, and Pierre Saramito, Numer Methods Partial Differential Eq 21(6) (2005), 1099–1121 included large portions that were copied from the following paper without proper citation: “Convergence and nonlinear stability of the Lagrange‐Galerkin method for the Navier‐Stokes equations,” Endre Suli, Numerische Mathematik, Vol. 53, No. 4, pp. 459–486 (July, 1988). We have retracted the paper and apologize to Dr. Suli Numer Methods Partial Differential Eq (2007)23(1)211 . 相似文献
20.
Me. Miansari D.D. Ganji Mo. Miansari 《Numerical Methods for Partial Differential Equations》2008,24(6):1361-1370
In this article, we try to obtain approximate Jacobi elliptic function solutions of the (1 + 1)‐dimensional long wave equation using Homotopy Perturbation Method. This method deforms a difficult problem into a simple problem which can be easily solved. In comparison with HPM, numerical methods leads to inaccurate results when the equation intensively depends on time, while He's method overcome the above shortcomings completely and can therefore be widely applicable in engineering. As a result, we obtain the approximate solution of the (1 + 1)‐dimensional long wave equation with initial conditions. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2008 相似文献