solving large systems arising from fractional models by preconditioned methods

Authors

reza khoshsiar ghaziani

shahrekord university mojtaba fardi

shahrekord university mehdi ghasemi

shahrekord university

abstract

this study develops and analyzes preconditioned krylov subspace methods to solve linear systemsarising 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.

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Journal title:
computational methods for differential equations

جلد ۳، شماره ۴، صفحات ۲۵۸-۲۷۳

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