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Numerical Solution for Elliptic Interface Problems Using Spectral Element Collocation Method [PDF]

Abstract and Applied Analysis, 2014
The aim of this paper is to solve an elliptic interface problem with a discontinuous coefficient and a singular source term by the spectral collocation method.
Peyman Hessari, Sang Dong Kim, Byeong-Chun Shin   +2 more
doaj   +3 more sources

Domain decomposition preconditioners for the spectral collocation method [PDF]

Journal of Scientific Computing, 1988
Several block iteration preconditioners are proposed and analyzed for the solution of elliptic problems by spectral collocation methods in a region partitioned into several rectangles.
Quarteroni, Alfio, Sacchilandriani, Giovanni   +1 more
core   +4 more sources

Space–time spectral collocation method for Klein–Gordon equation [PDF]

Journal of Algorithms & Computational Technology, 2021
By using the Legendre–Laguerre collocation method, we can construct a spectral collocation scheme to solve the Klein–Gordon equation on the half-line.
Ping Zhang, Te Li, Yuan-Hao Zhang
doaj   +2 more sources

Spectral collocation method for convection-diffusion equation

Demonstratio Mathematica
Spectral collocation method, named linear barycentric rational interpolation collocation method (LBRICM), for convection-diffusion (C-D) equation with constant coefficient is considered.
Li Jin, Cheng Yongling
doaj   +2 more sources

A M\"untz-Collocation spectral method for weakly singular volterra integral equations [PDF]

Journal of Scientific Computing, 2019
In this paper we propose and analyze a fractional Jacobi-collocation spectral method for the second kind Volterra integral equations (VIEs) with weakly singular kernel $(x-s)^{-\mu ...
Azaiez, Mejdi, Hou, Dianming, Lin, Yumin, Xu, Chuanju   +3 more
core   +5 more sources

Spectral-Collocation Methods for Fractional Pantograph Delay-Integrodifferential Equations [PDF]

Advances in Mathematical Physics, 2013
We propose and analyze a spectral Jacobi-collocation approximation for fractional order integrodifferential equations of Volterra type with pantograph delay. The fractional derivative is described in the Caputo sense. We provide a rigorous error analysis
Yin Yang, Yunqing Huang
doaj   +3 more sources

Binary spectral collocation method for the nonlinear Fokker-Planck equation

Journal of Algorithms & Computational Technology
A mixed Laguerre-Legendre spectral collocation schemes is constructed for initial-boundary value problem of the nonlinear Fokker-Planck nonhomogeneous equations and the linear Fokker-Planck homogeneous equation by using the Laguerre interpolation ...
Zhang Yajin, Wang Tianjun, Tan Jia
doaj   +2 more sources

Superconvergence of spectral collocation method for initial value problem of ordinary differential equations

上海师范大学学报. 自然科学版, 2021
In this paper, we study the spectral collocation method for the initial value problems of ordinary differential equations. Based on Legendre-Gauss points, we propose the spectral collocation method for the initial value problems of first-order and second-
QIAN Yiyun, ZHA Yuanyuan, CAI Kangwen, LIU Yanqin, WANG Xinyi, YI Lijun   +5 more
doaj   +1 more source

Spectral collocation methods [PDF]

Applied Numerical Mathematics, 1989
This is a survey article on the application of spectral collocation methods to the solution of partial differential equations. For the most part, the basis functions used are either trigonometric or Chebyshev polynomials, although there is some discussion of Legendre polynomials.
Hussaini, M. Y., Kopriva, D. A., Patera, A. T.   +2 more
openaire   +2 more sources

Space-time spectral collocation method for Allen-Cahn equation

上海师范大学学报. 自然科学版, 2023
Allen-Cahn equation is an important phase field model, which has been widely used to investigate interfacial dynamic problems. In this paper, we propose a Legendre-Gauss spectral collocation scheme for the Allen-Cahn equation by using Legendre-Gauss ...
JIA Mengshu, XIE Shanshan, JIAO Yujian
doaj   +1 more source