共查询到20条相似文献，搜索用时 0 毫秒
1.
H. Jafari A. Borhanifar S.A. Karimi 《Numerical Methods for Partial Differential Equations》2009,25(5):1231-1237
In this article, the sine–cosine, the standard tanh and the extended tanh methods has been used to obtain solutions of the bad Boussinesq and good Boussinesq equations. New solitions and periodic solutions are formally derived. The change of parameters, that will drastically change characteristics of the equation, is examined. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2009 相似文献
2.
3.
D. G. Natsis 《Numerical Algorithms》2007,44(3):281-289
In this paper we derive an analytical solution of the one-dimensional Boussinesq equations, in the case of waves relatively
long, with small amplitudes, in water of varying depth. To derive the analytical solution we first assume that the solution
of the model has a prescribed wave form, and then we obtain the wave velocity, the wave number and the wave amplitude. Finally
a specific application for some realistic values of wave parameters is given and a graphical presentation of the results is
provided.
相似文献
4.
To certain nonlinear evolution equations, the tanh method has been generalized for constructing not only solitary-wave but also soliton-like solutions. In this paper, no loss of conciseness, we further extend the generalized tanh method with computerized symbolic computation to a pair of generalized Hamiltonian equations. A new family of soliton-like analytical solutions is obtained, of which the solitary waves and previously-claimed soliton-like solutions are shown to be the special cases. 相似文献
5.
The paper deals with the analysis of pair diffusion models in semiconductor technology. The underlying model contains reaction‐drift‐diffusion equations for the mobile point defects and dopant‐defect pairs as well as reaction equations for immobile dopants which are coupled with a non‐linear Poisson equation for the chemical potential of the electrons. For homogeneous structures we present an existence and uniqueness result for strong solutions. Starting with energy estimates we derive further a priori estimates such that fixed point arguments due to Leray–Schauder guarantee the solvability of the model equations. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
6.
S.S. Ravindran 《Numerical Methods for Partial Differential Equations》2011,27(6):1639-1665
In this article, we study error estimates for approximate solutions of POD Galerkin type for the equations for the motion of a nonstationary viscous thermally conducting fluid in a bounded domain. Time discretization is based on backward Euler scheme. We study both the fully implicit and semi‐implicit versions of this scheme. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27 : 1639‐1665, 2011 相似文献
7.
We study an optimization based domain decomposition method for the Boussinesq equations governing natural convection problems. Domain decomposition is cast into a constrained minimization problem for which the objective functional measures the jump in the dependent variables across the interface between solid and fluid subdomains. We showthat solutions of the minimization problem exist and derive an optimality system from which these solutions may be determined. Finite element approximations of the solutions of the optimality system are examined. The domain decomposition method is also reformulated as a nonlinear least‐squares problem and the results of some numerical experiments are given. © 2002 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 18: 1–25, 2002 相似文献
8.
Salim A. Messaoudi Belkacem Said Houari 《Mathematical Methods in the Applied Sciences》2004,27(14):1687-1696
In this paper we consider the non‐linear wave equation a,b>0, associated with initial and Dirichlet boundary conditions. We prove, under suitable conditions on α,β,m,p and for negative initial energy, a global non‐existence theorem. This improves a result by Yang (Math. Meth. Appl. Sci. 2002; 25 :825–833), who requires that the initial energy be sufficiently negative and relates the global non‐existence of solutions to the size of Ω. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
9.
Elvira Barbera Carmela Currò Giovanna Valenti 《Mathematical Methods in the Applied Sciences》2010,33(12):1504-1515
A hyperbolic predator–prey model is proposed within the context of extended thermodynamics. The nature of the steady state solutions for the uniform and non‐uniform perturbations are analyzed. The existence of smooth traveling wave‐like solutions, related to the invasion of the predator population into a prey‐only state is discussed. Validation of the model in point is also accomplished by searching for numerical solutions of the system, which also points out limit cycles in the populations. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
10.
《Numerical Methods for Partial Differential Equations》2018,34(2):731-759
In this article, an efficient hybrid method has been developed for solving some special type of nonlinear partial differential equations. Hybrid method is based on tanh–coth method, quasilinearization technique and Haar wavelet method. Nonlinear partial differential equations have been converted into a nonlinear ordinary differential equation by choosing some suitable variable transformations. Quasilinearization technique is used to linearize the nonlinear ordinary differential equation and then the Haar wavelet method is applied to linearized ordinary differential equation. A tanh–coth method has been used to obtain the exact solutions of nonlinear ordinary differential equations. It is easier to handle nonlinear ordinary differential equations in comparison to nonlinear partial differential equations. A distinct feature of the proposed method is their simple applicability in a variety of two‐ and three‐dimensional nonlinear partial differential equations. Numerical examples show better accuracy of the proposed method as compared with the methods described in past. Error analysis and stability of the proposed method have been discussed. 相似文献
11.
We consider an anisotropic phase‐field model for the isothermal solidification of a binary alloy due to Warren–Boettinger ( Acta. Metall. Mater. 1995; 43 (2):689). Existence of weak solutions is established under a certain convexity condition on the strongly non‐linear second‐order anisotropic operator and Lipschitz and boundedness assumptions for the non‐linearities. A maximum principle holds that guarantees the existence of a solution under physical assumptions on the non‐linearities. The qualitative properties of the solutions are illustrated by a numerical example. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
12.
Caidi Zhao 《Mathematical Methods in the Applied Sciences》2013,36(7):840-856
This paper studies the approximation of the non‐Newtonian fluid equations by the artificial compressibility method. We first introduce a family of perturbed compressible non‐Newtonian fluid equations (depending on a positive parameter ε) that approximates the incompressible equations as ε → 0+. Then, we prove the unique existence and convergence of solutions for the compressible equations to the solutions of the incompressible equations. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
13.
Yuming Qin Xinguang Yang Yu‐Zhu Wang Xin Liu 《Mathematical Methods in the Applied Sciences》2012,35(3):278-285
In this paper, we investigate three‐dimensional incompressible Boussinesq equations and establish some logarithmically improved blow‐up criteria of smooth solutions to the Cauchy problem for the incompressible Boussinesq equations. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
14.
Hyung-Chun Lee Byeong Chun Shin 《Journal of Mathematical Analysis and Applications》2002,273(2):457-479
The long-time behavior of solutions for an optimal distributed control problem associated with the Boussinesq equations is studied. First, a quasi-optimal solution for the Boussinesq equations is constructed; this quasi-optimal solution possesses the decay (in time) properties. Then, some preliminary estimates for the long-time behavior of all solutions of the Boussinesq equations are derived. Next, the existence of a solution for the optimal control problem is proved. Finally, the long-time decay properties for the optimal solutions is established. 相似文献
15.
This article presents the general case‐study of our previous works regarding generalized Boussinesq equations [17, 18, 19], that focus on application of various subordinate methods where are applied to construct more general exact solutions of the coupled Boussinesq equations. In this article, the ‐expansion method is applied on coupled Boussinesq equations. Our work is motivated by the fact that the ‐expansion method provides not only more general forms of solutions but also periodic, solitary waves, and rational solutions. The method appears to be easier and faster by means of a symbolic manipulation program. © 2016 Wiley Periodicals, Inc. Complexity 21: 151–155, 2016 相似文献
16.
Christian Klein;Jean-Claude Saut; 《Studies in Applied Mathematics》2024,153(1):e12691
The aim of this paper is to present a survey and a detailed numerical study on a remarkable Boussinesq system describing weakly nonlinear, long surface water waves. In the one-dimensional case, this system can be viewed as a dispersive perturbation of the hyperbolic Saint-Venant (shallow water) system. The asymptotic stability of the solitary waves is numerically established. Blow-up of solutions for initial data not satisfying the noncavitation condition as well as the appearance of dispersive shock waves are studied. 相似文献
17.
In this paper, analytic solutions of the variant Boussinesq equations are obtained by the homotopy analysis and the homotopy Pad methods. The obtained approximation using homotopy method contains an auxiliary parameter, which is a simple way to control and adjust the convergence region and rate of solution series. The approximation solutions by [m,m] homotopy Pad technique is often independent of auxiliary parameter , and this technique accelerates the convergence of the related series. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
18.
S. S. Motsa P. Sibanda S. Shateyi 《Mathematical Methods in the Applied Sciences》2011,34(11):1406-1413
We propose a new quasi‐linearization technique for solving systems of nonlinear equations. The method finds recursive formulae for higher order deformation equations which are then solved using the Chebyshev spectral collocation method. The implementation of the method is demonstrated by solving the coupled nonlinear equations that govern the injection of a non‐Newtonian fluid through the sides of a vertical channel. The equations are also solved numerically and comparison made with the results in the literature. The linearization method is found to be computationally efficient and accurate with a rapidly convergent series solution. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
19.
Jianhua Chen Xianhua Tang Zu Gao 《Mathematical Methods in the Applied Sciences》2017,40(14):5056-5067
In this paper, we prove the existence of ground state sign‐changing solutions for the following class of elliptic equation: where , and K(x) are positive continuous functions. Firstly, we obtain one ground state sign‐changing solution ub by using some new analytical skills and non‐Nehari manifold method. Furthermore, the energy of ub is strictly larger than twice that of the ground state solutions of Nehari type. We also establish the convergence property of ub as the parameter b↘0. Copyright © 2017 John Wiley & Sons, Ltd. 相似文献
20.
Handan Borluk Gulcin M. Muslu 《Numerical Methods for Partial Differential Equations》2015,31(4):995-1008
In this article, we propose a Fourier pseudospectral method for solving the generalized improved Boussinesq equation. We prove the convergence of the semi‐discrete scheme in the energy space. For various power nonlinearities, we consider three test problems concerning the propagation of a single solitary wave, the interaction of two solitary waves and a solution that blows up in finite time. We compare our numerical results with those given in the literature in terms of numerical accuracy. The numerical comparisons show that the Fourier pseudospectral method provides highly accurate results. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 995–1008, 2015 相似文献