A Fast Spectral Collocation Method for Two Sided Space Fractional Equation

机译：两侧空间分数阶方程的快速谱配置方法

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This paper provides a fast polynomial spectral collocation method for the two sided space fractional equation, and the time discretization is based on the fractional step procedure in two dimensional cases. By combining the general Jacobi polynomial approximation and Lagrange interpolation, the computational cost is considerably reduced for both generating the deferential matrices and approximating solutions in the multi-dimensional cases. The formulae of the matrices for left and right Riemann-Liouville fractional derivatives and ˉrst order classical derivative are presented. The procedures on the one dimensional and two dimensional linear cases are detailedly discussed. Finally, several numerical experiments demonstrate the e±ciency and spectra convergence of the present method.

机译：该文为两侧空间分数阶方程提供了一种快速的多项式谱配点方法，在二维情况下，时间离散化基于分数阶跃过程。通过将一般的Jacobi多项式逼近和Lagrange插值相结合，在多维情况下生成微分矩阵和逼近解都大大降低了计算成本。给出了左右黎曼分式和一阶经典导数的矩阵公式。详细讨论了一维和二维线性情况下的过程。最后，几个数值实验证明了本方法的效率和光谱收敛性。

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来源
《Proceedings of the Fifth symposium on fractional differentiation and its applications》|2012年|1-6|共6页
会议地点 Nanjing(CN)
作者
Weihua Deng; Lijing Zhao;
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作者单位

School of Mathematics and Statistics, Lanzhou University, Lanzhou,730000, P.R.China;

School of Mathematics and Statistics, Lanzhou University, Lanzhou, 730000, P.R.China;

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会议组织
原文格式 PDF
正文语种 eng
中图分类数学;
关键词
Two sides; spectral collocation; fractional step; general Jacobi polynomials; Riemann-Liouville fractional derivative.;

机译：两侧;谱配点;分数阶;一般Jacobi多项式; Riemann-Liouville分数阶导数;

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A Fast Spectral Collocation Method for Two Sided Space Fractional Equation

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