共查询到20条相似文献,搜索用时 15 毫秒
1.
Jian Chen Zhongying Chen Sirui Cheng Jiemin Zhan 《Numerical Methods for Partial Differential Equations》2015,31(5):1665-1691
In this article, multilevel augmentation method (MAM) for solving the Burgers' equation is developed. The Crank–Nicolson–Galerkin scheme of the Burgers' equation results in nonlinear algebraic systems at each time step, the computational cost for solving these nonlinear systems is huge. The MAM allows us to solve the nonlinear system at a fixed initial lower level and then compensate the error by solving a linear system at the higher level. We prove that the method has the same optimal convergence order as the projection method, while reducing the computational complexity greatly. Finally, numerical experiments are presented to confirm the theoretical analysis and illustrate the efficiency of the proposed method. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1665–1691, 2015 相似文献
2.
A differential quadrature based numerical method for highly accurate solutions of Burgers' equation 下载免费PDF全文
V. S. Aswin Ashish Awasthi Mohammad Mehdi Rashidi 《Numerical Methods for Partial Differential Equations》2017,33(6):2023-2042
In this article, we introduce a new, simple, and accurate computational technique for one‐dimensional Burgers' equation. The idea behind this method is the use of polynomial based differential quadrature (PDQ) for the discretization of both time and space derivatives. The quasilinearization process is used for the elimination of nonlinearity. The resultant scheme has simulated for five classic examples of Burgers' equation. The simulation outcomes are validated through comparison with exact and secondary data in the literature for small and large values of kinematic viscosity. The article has deduced that the proposed scheme gives very accurate results even with less number of grid points. The scheme is found to be very simple to implement. Hence, it applies to any domain requires quick implementation and computation.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 2023–2042, 2017 相似文献
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A new method for the solution of the damped Burgers' equation is described. The marker method relies on the definition of a convective field associated with the underlying partial differential equation; the information about the approximate solution is associated with the response of an ensemble of markers to this convective field. Some key aspects of the method, such as the selection of the shape function and the initial loading, are discussed in some details. The marker method is applicable to a general class of nonlinear dispersive partial differential equations. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006 相似文献
4.
Ankita Shukla Mani Mehra Günter Leugering 《Mathematical Methods in the Applied Sciences》2020,43(13):7595-7614
Water wave propagation in an open channel network can be described by the viscous Burgers' equation on the corresponding connected graph, possibly with small viscosity. In this paper, we propose a fast adaptive spectral graph wavelet method for the numerical solution of the viscous Burgers' equation on a star-shaped connected graph. The vital feature of spectral graph wavelets is that they can be constructed on any complex network using the graph Laplacian. The essence of the method is that the same operator can be used for the construction of the spectral graph wavelet and the approximation of the differential operator involved in the Burgers' equation. In this paper, two test problems are considered with homogeneous Dirichlet boundary condition. The numerical results show that the method accurately captures the evolution of the localized patterns at all the scales, and the adaptive node arrangement is accordingly obtained. The convergence of the given method is verified, and efficiency is shown using CPU time. 相似文献
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Peter Lewis David Nualart 《Stochastics An International Journal of Probability and Stochastic Processes》2018,90(7):1053-1086
In this project, we investigate the stochastic Burgers' equation with multiplicative space-time white noise on an unbounded spatial domain. We give a random field solution to this equation by defining a process via a kind of Feynman–Kac representation which solves a stochastic partial differential equation such that its Hopf–Cole transformation solves Burgers' equation. Finally, we obtain Hölder regularity and moment estimates for the solution to Burgers' equation. 相似文献
7.
Dia Zeidan Chi Kin Chau Tzon-Tzer Lu Wei-Quan Zheng 《Mathematical Methods in the Applied Sciences》2020,43(5):2171-2188
In this paper, a novel Adomian decomposition method (ADM) is developed for the solution of Burgers' equation. While high level of this method for differential equations are found in the literature, this work covers most of the necessary details required to apply ADM for partial differential equations. The present ADM has the capability to produce three different types of solutions, namely, explicit exact solution, analytic solution, and semi-analytic solution. In the best cases, when a closed-form solution exists, ADM is able to capture this exact solution, while most of the numerical methods can only provide an approximation solution. The proposed ADM is validated using different test cases dealing with inviscid and viscous Burgers' equations. Satisfactory results are obtained for all test cases, and, particularly, results reported in this paper agree well with those reported by other researchers. 相似文献
8.
Yusuf Uar Nuri M. Yamurlu hsan elikkaya 《Numerical Methods for Partial Differential Equations》2019,35(2):478-492
The aim of this study is to obtain numerical behavior of a one‐dimensional modified Burgers' equation using cubic B‐spline collocation finite element method after splitting the equation with Strang splitting technique. Moreover, the Ext4 and Ext6 methods based on Strang splitting and derived from extrapolation have also been applied to the equation. To observe how good and effective this technique is, we have used the well‐known the error norms L2 and L∞ in the literature and compared them with previous studies. In addition, the von Neumann (Fourier series) method has been applied after the nonlinear term has been linearized to investigate the stability of the method. 相似文献
9.
The combined approach of linearization and splitting up is used for devising new algorithms to solve a one-dimensional Burgers' equation. Two schemes are discussed and the computed solutions are compared with the exact solution. For this problem it is found that the schemes proposed yield excellent numerical results for Reynolds number R ranges from 50 up to 1500. The schemes were also tested for another problem whose R = 10000. In this case a filtering technique is used to overcome the nonlinear instability. 相似文献
10.
Reza Mohammadi 《Applicable analysis》2013,92(12):2189-2215
A numerical method based on exponential spline and finite difference approximations is developed to solve the generalized Burgers'-Fisher equation. The error analysis, stability and convergence properties of the method are studied via energy method. The method is shown to be unconditionally stable and accurate of orders 𝒪(k?+?kh?+?h 2) and 𝒪(k?+?kh?+?h 4). Some test problems are given to demonstrate the applicability of the purposed method numerically. Numerical results verify the theoretical behaviour of convergence properties. The main superiority of the presented scheme is its simplicity and applicability in comparison with the existing well-known methods. 相似文献
11.
Alev Kelleci Ahmet Yıldırım 《Numerical Methods for Partial Differential Equations》2011,27(4):982-995
In this study, we combined homotopy perturbation and Pade techniques for solving homogeneous and inhomogeneous two‐dimensional parabolic equation. Also, we apply our combined method for coupled Burgers' equations. The numerical results demonstrate that our combined method gives the approximate solution with faster convergence rate and higher accuracy than using the classic homotopy perturbation method. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27: 982–995, 2011 相似文献
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Soyoon Bak 《Numerical Methods for Partial Differential Equations》2019,35(5):1756-1776
In this study, new high‐order backward semi‐Lagrangian methods are developed to solve nonlinear advection–diffusion type problems, which are realized using high‐order characteristic‐tracking strategies. The proposed characteristic‐tracking strategies are second‐order L‐stable and third‐order L(α)‐stable methods, which are based on a classical implicit multistep method combined with a error‐correction method. We also use backward differentiation formulas and the fourth‐order finite‐difference scheme for diffusion problem discretization in the temporal and spatial domains, respectively. To demonstrate the adaptability and efficiency of these time‐discretization strategies, we apply these methods to nonlinear advection–diffusion type problems such as the viscous Burgers' equation. Through simulations, not only the temporal and spatial accuracies are numerically evaluated but also the proposed methods are shown to be superior to the compared existing characteristic‐tracking methods under the same rates of convergence in terms of accuracy and efficiency. Finally, we have shown that the proposed method well preserves the energy and mass when the viscosity coefficient becomes zero. 相似文献
15.
《Applied Mathematical Modelling》2001,25(9):731-741
A finite element approximation of the two-dimensional steady Burgers' equation is presented and a conjugate gradient approach is taken to solve the resulting finite element equations. The scheme is computationally efficient and is relatively easy to implement. An optimal error bound is established and a set of test problems with known analytic solutions is given to demonstrate the efficiency of the method. 相似文献
16.
Haifeng Wang Da Xu Jun Zhou Jing Guo 《Numerical Methods for Partial Differential Equations》2021,37(1):732-749
In this article, we use the weak Galerkin (WG) finite element method to study a class of time fractional generalized Burgers' equation. The existence of numerical solutions and the stability of fully discrete scheme are proved. Meanwhile, by applying the energy method, an optimal order error estimate in discrete L2 norm is established. Numerical experiments are presented to validate the theoretical analysis. 相似文献
17.
In this article, a new compact difference scheme is proposed in exponential form to solve two-dimensional unsteady nonlinear Burgers' and Navier-Stokes
equations of motion in polar cylindrical coordinates by using half-step discretization. At each time level by using only nine grid points in space, the proposed scheme
gives accuracy of order four in space and two in time. The method is directly applicable to the equations having singularities at boundary points. Stability analysis
is explained in detail and many benchmark problems like Burgers', Navier-Stokes
and Taylor-vortex problems in polar cylindrical coordinates are solved to verify the
accuracy and efficiency of the scheme. 相似文献
18.
This paper derives analytical solutions for the two dimensional and the three dimensional Burgers' equation. The two-dimensional and three-dimensional Burgers' equation are defined in a square and a cubic space domain, respectively, and a particular set of boundary and initial conditions is considered. The analytical solution for the two dimensional Burgers' equation is given by the quotient of two infinite series which involve Bessel, exponential, and trigonometric functions. The analytical solution for the three dimensional Burgers' equation is given by the quotient of two infinite series which involve hypergeometric, exponential, trigonometric and power functions. For both cases, the solutions can describe shock wave phenomena for large Reynolds numbers (Re ≥ 100), which is useful for testing numerical methods. 相似文献
19.
Raphaël Rebelo Francis Valiquette 《Journal of Difference Equations and Applications》2013,19(5):738-757
The method of equivariant moving frames is used to construct symmetry preserving finite difference schemes of partial differential equations invariant under finite-dimensional symmetry groups. Invariant numerical schemes for a heat equation with logarithmic source and the spherical Burgers' equation are obtained. Numerical tests show how invariant schemes can be more accurate than standard discretizations. 相似文献
20.
We apply the least‐squares finite element method with adaptive grid to nonlinear time‐dependent PDEs with shocks. The least‐squares finite element method is also used in applying the deformation method to generate the adaptive moving grids. The effectiveness of this method is demonstrated by solving a Burgers' equation with shocks. Computational results on uniform grids and adaptive grids are compared for the purpose of evaluation. The results show that the adaptive grids can capture the shock more sharply with significantly less computational time. For moving shock, the adaptive grid moves correctly with the shock. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006 相似文献