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131.
《国际计算机数学杂志》2012,89(3-4):271-286
This paper presents techniques for the numerical solution of partial differential equations using cubic spline collocation. The main spline relations are presented and incorporated into solution procedures for partial differential equations. The computational algorithm in every case is a tridiagonal matrix system amenable to efficient inversion methods. Truncation errors and stability are briefly discussed. Finally, some examples of their application to parabolic and hyperbolic systems with mixed boundary conditions are presented. The results obtained are encouraging and justify further research in this field. 相似文献
132.
《国际计算机数学杂志》2012,89(1):93-104
In this paper, the Chebyshev matrix method is applied generalisations of the Hermite, Laguerre, Legendre and Chebyshev differential equations which have polynomial solution. The method is based on taking the truncated Chebyshev series expansions of the functions in equation, and then substituting their matrix forms into the result equation. Thereby the given equation reduces to a matrix equation, which corresponds to a system of linear algebraic equations with unknown Chebyshev coefficients. 相似文献
133.
《国际计算机数学杂志》2012,89(1-4):243-267
Large sparse nonsymmetric problems of the form A u = b are frequently solved using restarted conjugate gradient-type algorithms such as the popular GCR and GMRES algorithms. In this study we define a new class of algorithms which generate the same iterates as the standard GMRES algorithm but require as little as half of the computational expense. This performance improvement is obtained by using short economical three-term recurrences to replace the long recurrence used by GMRES. The new algorithms are shown to have good numerical properties in typical cases, and the new algorithms may be easily modified to be as numerically safe as standard GMRES. Numerical experiments with these algorithms are given in Part II, in which we demonstrate the improved performance of the new schemes on different computer architectures. 相似文献
134.
《国际计算机数学杂志》2012,89(15):1996-2018
In this article, we suggest a new third-order time discrete scheme for the two-dimensional non-stationary Navier–Stokes equations. After presenting the Galerkin finite element approximation for the spatial discretization, we consider an implicit/explicit time discrete scheme for the problem, which is based on the two-step Adams–Moulton scheme (implicit scheme) for the linear term and the three-step Adams–Bashforth scheme (explicit scheme) for the nonlinear term. In this method, we only need to solve a linearized discrete system at each time step, so the scheme can converge fast and the computational cost can be reduced. Moreover, under some assumptions, we deduce the stability and optimal error estimate for the velocity in L 2-norm. 相似文献
135.
136.
Allan P. Engsig-Karup Jan S. Hesthaven Harry B. Bingham Per A. Madsen 《Journal of Engineering Mathematics》2006,56(3):351-370
A discontinuous Galerkin finite-element method (DG-FEM) solution to a set of high-order Boussinesq-type equations for modelling
highly nonlinear and dispersive water waves in one horizontal dimension is presented. The continuous equations are discretized
using nodal polynomial basis functions of arbitrary order in space on each element of an unstructured computational domain.
A fourth-order explicit Runge-Kutta scheme is used to advance the solution in time. Methods for introducing artificial damping
to control mild nonlinear instabilities are also discussed. The accuracy and convergence of the model with both h (grid size) and p (order) refinement are confirmed for the linearized equations, and calculations are provided for two nonlinear test cases
in one horizontal dimension: harmonic generation over a submerged bar, and reflection of a steep solitary wave from a vertical
wall. Test cases for two horizontal dimensions will be considered in future work. 相似文献
137.
戴娟 《常州信息职业技术学院学报》2006,5(3):6-8
同余方程组是数论中一个极为有用的课题。文中考虑的是具有一个未知数而具有不同的模的一次同余方程组。一般可以用中国剩余定理或者递推算法等方法给出一次同余方程组的解法。利用矩阵的初等变换和矩阵的Sm ith标准形给出了求解一次同余方程组的一种矩阵解法。 相似文献
138.
Jiequan Li Guoxian Chen 《International journal for numerical methods in engineering》2006,65(6):834-862
This paper extends the generalized Riemann problem method (GRP) to the system of shallow water equations with bottom topography. The main contribution is that the generalized Riemann problem method (J. Comput. Phys. 1984; 55 (1):1–32) is used to evaluate the midpoint values of solutions at each cell interface so that the bottom topography effect is included in numerical fluxes, and at the same step the source term is discretized with an interface method in which only mid‐point values are plugged in. This scheme is well balanced between the flux gradient and bottom topography when incorporating the surface gradient method (SGM) (J. Comput. Phys. 2001; 168 (1):1–25) into data reconstruction step, and it is also suitable for both steady and unsteady flow simulations. We illustrate the accuracy of this scheme by several 1‐D and 2‐D numerical experiments. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
139.
Implicit integration schemes for elastoplastic constitutive equations have been developed in recent years as an alternative to explicit schemes. The consistent tangent constitutive matrix Dcon that results from implicit schemes makes the global stiffness matrix consistent with the implicit integration procedure and differs from the traditional continuum tangent constitutive matrix Dep that results from explicit schemes. Onset of strain localization and shear banding has been traditionally predicted using the continuum tangent constitutive matrix. It is shown that different criteria for onset of shear-band formation are obtained depending on whether Dcon or Dep is used. It is shown that shear band prediction using Dcon is step-size dependent, and that the use of Dcon influences the predicted onset of strain localization in frictional materials. An analytical equation for prediction of the onset of shear-band formation using Dcon for the Mohr–Coulomb model is developed, and a numerical example is presented. 相似文献
140.