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51.
1引言 在多种问题的数值模拟中均涉及抛物型对流扩散方程的数值求解问题.由于配置法 无需计算数值积分,计算简便,收敛阶高等优点,使之在工程技术和计算数学的许多领域 得到广泛的应用,但范围一般局限在一维常系数{1,21和二维常系数问题降,4],90年代[s] 提出了二维变系数 相似文献
52.
利用描述连续铸钢过程二冷区喷水控制下钢的热传导的半离散化模型 ,我们构造一包含温度梯度约束的最优控制问题 .针对此最优控制问题 ,采用直接配置法进行数值求解 ,得出相应的近似最优控制 . 相似文献
53.
54.
Hideaki Kaneko Richard D. Noren Peter A. Padilla 《Journal of Computational and Applied Mathematics》1997,80(2):351-349
In this paper, we analyse the iterated collocation method for Hammerstein equations with smooth and weakly singular kernels. The paper expands the study which began in [16] concerning the superconvergence of the iterated Galerkin method for Hammerstein equations. We obtain in this paper a similar superconvergence result for the iterated collocation method for Hammerstein equations. We also discuss the discrete collocation method for weakly singular Hammerstein equations. Some discrete collocation methods for Hammerstein equations with smooth kernels were given previously in [3, 18]. 相似文献
55.
In this paper, a new collocation BEM for the Robin boundary value problem of the conductivity equation ▽(γ▽u) = 0 is discussed, where the 7 is a piecewise constant function. By the integral representation formula of the solution of the conductivity equation on the boundary and interface, the boundary integral equations are obtained. We discuss the properties of these integral equations and propose a collocation method for solving these boundary integral equations. Both the theoretical analysis and the error analysis are presented and a numerical example is given. 相似文献
56.
该文讨论用Legendre拟谱方法数值求解非线性Cahn Hilliard方程的Dirichlet问题.建立了其半离散和全离散逼近格式,它们保持原问题能量耗散的性质.证明了离散解的存在唯一性,并给出了最佳误差估计.数值实验也证实了我们的结果. 相似文献
57.
Graeme Fairweather Heping Ma Weiwei Sun 《Numerical Methods for Partial Differential Equations》2008,24(2):449-464
An orthogonal spline collocation (OSC) spatial discretization is proposed for the solution of the fully coupled stream function‐vorticity formulation of the Navier–Stokes equations in two dimensions. For the time‐stepping, a three‐level leapfrog scheme is employed. This method is algebraically linear, and, at each time step, gives rise to a system of linear equations of the form arising in the OSC approximation of the biharmonic Dirichlet problem and can be solved by a fast direct method. Error estimates in the Hl–norm in space, l = 1,2, are derived for the semi‐discrete method and the fully‐discrete leapfrog scheme which is also shown to be second order accurate in time. Numerical results are presented which confirm the theoretical analysis and exhibit superconvergence phenomena, which provide superconvergent approximations to the components of the velocity. © John Wiley & Sons, Inc. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2008 相似文献
58.
M.T. Darvishi S. Kheybari F. Khani 《Communications in Nonlinear Science & Numerical Simulation》2008,13(10):2091-2103
In this paper, a numerical solution of the generalized Burgers–Huxley equation is presented. This is the application of spectral collocation method. To reduce roundoff error in this method we use Darvishi’s preconditionings. The numerical results obtained by this method have been compared with the exact solution. It can be seen that they are in a good agreement with each other, because errors are very small and figures of exact and numerical solutions are very similar. 相似文献
59.
In this paper we give necessary and sufficient conditions for convergence of continuous collocation approximations of solutions of first kind Volterra integral equations. The results close some longstanding gaps in the theory of polynomial spline collocation methods for such equations. The convergence analysis is based on a Runge-Kutta or ODE approach.
60.
In this paper we introduce and study polynomial spline collocation methods for systems of Volterra integral equations with unknown lower integral limit arising in mathematical economics. Their discretization leads to implicit Runge-Kutta-type methods. The global convergence and local superconvergence properties of these methods are proved, and the theory is illustrated by a numerical example arising in the application of such equations in certain mathematical models of liquidation. 相似文献