Faculty of Mathematical Sciences, Shahrekord University, P. O. Box 115, Shahrekord, Iran
Abstract
This study develops and analyzes preconditioned Krylov subspace methods to solve linear systems arising from discretization of the time-independent space-fractional models. First, we apply shifted Grunwald formulas to obtain a stable finite difference approximation to fractional advection-diffusion equations. Then, we employee two preconditioned iterative methods, namely, the preconditioned generalized minimal residual (preconditioned GMRES) method and the preconditioned conjugate gradient for normal residual( preconditioned CGN) method, to solve the corresponding discritized systems. We further make comparisons between the preconditioners commonly used in the parallelization of the preconditioned Krylov subspace methods. The results suggest that preconditioning technique is a promising candidate for solving large-scale linear systems arising from fractional models.
Khoshsiar Ghaziani, R., Fardi, M., & Ghasemi, M. (2015). Solving large systems arising from fractional models by preconditioned methods. Computational Methods for Differential Equations, 3(4), 258-273.
MLA
Reza Khoshsiar Ghaziani; Mojtaba Fardi; Mehdi Ghasemi. "Solving large systems arising from fractional models by preconditioned methods". Computational Methods for Differential Equations, 3, 4, 2015, 258-273.
HARVARD
Khoshsiar Ghaziani, R., Fardi, M., Ghasemi, M. (2015). 'Solving large systems arising from fractional models by preconditioned methods', Computational Methods for Differential Equations, 3(4), pp. 258-273.
VANCOUVER
Khoshsiar Ghaziani, R., Fardi, M., Ghasemi, M. Solving large systems arising from fractional models by preconditioned methods. Computational Methods for Differential Equations, 2015; 3(4): 258-273.
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