نتایج جستجو برای Collocation method

تعداد نتایج: 1070041  

2014
Junghan Kim, Wonkyu Chung, Sunyoung Bu, Philsu Kim,

In this paper, we introduce a generalized Chebyshev collocation method (GCCM) based on the generalized Chebyshev polynomials for solving stiff systems. For employing a technique of the embedded Runge-Kutta method used in explicit schemes, the property of the generalized Chebyshev polynomials is used, in which the nodes for the higher degree polynomial are overlapped with those for the lower deg...

Journal: :SIAM J. Scientific Computing 2014
Mohsen Zayernouri, George E. Karniadakis,

We develop an exponentially accurate fractional spectral collocation method for solving steady-state and time-dependent fractional PDEs (FPDEs). We first introduce a new family of interpolants, called fractional Lagrange interpolants, which satisfy the Kronecker delta property at collocation points. We perform such a construction following a spectral theory recently developed in [M. Zayernouri ...

M. Parvizi, M. R. Eslahchi,

In this paper we present a new method to find simple or multiple roots of functions in a finite interval. In this method using bisection method we can find an interval such that this function is one to one on it, thus we can transform problem of finding roots in this interval into an ordinary differential equation with boundary conditions. By solving this equation using collocation method we ca...

2009
Zhanyi Liu, Haifeng Wang, Hua Wu, Sheng Li,

Statistical bilingual word alignment has been well studied in the context of machine translation. This paper adapts the bilingual word alignment algorithm to monolingual scenario to extract collocations from monolingual corpus. The monolingual corpus is first replicated to generate a parallel corpus, where each sentence pair consists of two identical sentences in the same language. Then the mon...

1995
Weizhang Huang, Robert D. Russell,

A new moving mesh method is introduced for solving time dependent partial diierential equations (PDEs) in divergence form. The method uses a cell-averaging cubic Hermite collocation discretization for the physical PDEs and a three point nite diierence discretization for the PDE which determines the moving mesh. Numerical results are presented for a selection of diicult benchmark problems, inclu...

2016
Mohammad Ali Fariborzi Araghi, Amir Fallahzadeh,

In this paper, the inherited collocation method is introduced to solve the fuzzy differential equations. For this purpose, the so-called inherited LU factorization of matrices and inherited polynomials are used to decompose the extended crisp matrix obtained from the proposed method easily. The examples show the efficiency and importance of this method.

2009
Michael J. Johnson, Georg Heinig,

Symmetric collocation, which can be used to numerically solve linear partial differential equations, is a natural generalization of the well-established scattered data interpolation method known as radial basis function (rbf) interpolation. As with rbf interpolation, a major shortcoming of symmetric collocation is the high cost, in terms of floating point operations, of evaluating the obtained ...

Journal: :IJCSM 2009
Alexander G. Ramm,

A collocation method is formulated and justified for numerical solution of the Fredholm second-kind integral equations. As an application the Lippmann-Schwinger equation is considered. The results obtained provide an error estimate and a justification of the limiting procedure used in the earlier papers by the author, dealing with many-body scattering problems in the case of small scatterers, a...

Journal: :J. Comput. Physics 2015
Alireza Nejadmalayeri, Alexei Vezolainen, Eric Brown-Dymkoski, Oleg V. Vasilyev,

a r t i c l e i n f o a b s t r a c t Dynamic load balancing Wavelets Lifting scheme Second generation wavelets Adaptive grid Multiresolution Multilevel method Multigrid method Numerical method Partial differential equations Elliptic problem A parallel adaptive wavelet collocation method for solving a large class of Partial Differential Equations is presented. The parallelization is achieved by...

Journal: :J. Sci. Comput. 2008
Zhimin Zhang,

We reveal the relationship between a Petrov–Galerkin method and a spectral collocation method at the Chebyshev points of the second kind (±1 and zeros of Uk) for the two-point boundary value problem. Derivative superconvergence points are identified as the Chebyshev points of the first kind (Zeros of Tk). Super-geometric convergent rate is established for a special class of solutions.

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