Space-time spectral method for a weakly singular parabolic partial integro-differential equation on irregular domains

被引:44
作者
Fakhar-Izadi, Farhad [1 ]
Dehghan, Mehdi [1 ]
机构
[1] Amirkabir Univ Technol, Fac Math & Comp Sci, Dept Appl Math, Tehran 15914, Iran
关键词
Weakly singular partial integro-differential equation; Nodal spectral element method; Legendre-spectral method; Gauss quadrature formulas; Sylvester matrix equation; FINITE-ELEMENT METHODS; COLLOCATION METHODS; NUMERICAL-SOLUTION; APPROXIMATIONS; DIFFUSION; INTERPOLATION; INTEGRATION;
D O I
10.1016/j.camwa.2014.03.016
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The spectral method is proposed for the partial integro-differential equations with a weakly singular kernel on irregular domains. The space discretization is based on the nodal spectral element method using the Lagrange polynomials basis associated with the Gauss-Lobatto-Legendre quadrature nodes. Also the model is discretized in time with the Legendre spectral Galerkin method. The discretization leads to conversion of the problem to a Sylvester matrix equation which can be solved efficiently by the QZ algorithm (Gardiner et al., 1992). The convergence of the method is proven by providing a priori L-2-error estimate. Numerical results illustrate the efficiency and spectral accuracy of the proposed method. (C) 2014 Elsevier Ltd. All rights reserved.
引用
收藏
页码:1884 / 1904
页数:21
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