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Solving large systems arising from fractional models by preconditioned methods | ||
| Computational Methods for Differential Equations | ||
| مقاله 3، دوره 3، شماره 4، دی 2015، صفحه 258-273 اصل مقاله (350.05 K) | ||
| نوع مقاله: Research Paper | ||
| نویسندگان | ||
| Reza Khoshsiar Ghaziani* ؛ Mojtaba Fardi؛ Mehdi Ghasemi | ||
| Faculty of Mathematical Sciences, Shahrekord University, P. O. Box 115, Shahrekord, Iran | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Krylov subspace methods؛ . Preconditioning techniques؛ Fractional model | ||
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