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A space‐time spectral collocation method for the 2‐dimensional nonlinear Riesz space fractional diffusion equations
Author(s) -
Li Hui,
Jiang Wei
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5124
Subject(s) - mathematics , spectral method , collocation (remote sensing) , mathematical analysis , discretization , collocation method , legendre polynomials , nonlinear system , orthogonal collocation , fractional calculus , differential equation , ordinary differential equation , physics , remote sensing , quantum mechanics , geology
The space‐time spectral collocation method was initially presented for the 1‐dimensional sine‐Gordon equation. In this article, we introduce a space‐time spectral collocation method for solving the 2‐dimensional nonlinear Riesz space fractional diffusion equations. The method is based on a Legendre‐Gauss‐Lobatto spectral collocation method for discretizing spatial and the spectral collocation method for the time nonlinear first‐order system of ordinary differential equation. Optimal priori error estimates in L 2 norms for the semidiscrete formulation and the uniqueness of the approximate solution are derived. The method has spectral accuracy in both space and time, and the numerical results confirm the statement.