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W. McLean ; Vidar Thomée (Institutionen för matematiska vetenskaper, matematik)
Journal of Integral Equations and Applications (0897-3962). Vol. 22 (2010), 1, p. 57-94.
[Artikel, refereegranskad vetenskaplig]

We consider the discretization in time if a fractional order diffusion equation. The approximation is based on a further development of the approach of using Laplace transformation to represent the solution as a contour integral, evaluated to high accuracy by quadrature. This technique reduces the problem to a finite set of elliptic equations with complex coefficients, which may be solved in parallel. Three different methods, using 2N + 1 quadrature points, are discussed. The first has an error of order O (e(-cN)) away from t = 0, whereas the second and third methods are uniformly accurate of order O (e(-C root N)). Unlike the first and second methods, the third method does not use the Laplace transform of the forcing term. The basic analysis of the time discretizaiton takes place in a Banach space setting and uses a resolvent esitmate for the associated elliptic operator. The methods are combined with finite element discretization in the spatial variable to yield fully discrete methods.

Nyckelord: Fractional order diffusion equation, Laplace transformation, resolvent, quadrature, spatially semidiscreted approximation, finite elements, time-discretization, memory term, parallel method, diffusion, stability, spaces, quadrature, inversion

Denna post skapades 2010-05-05.
CPL Pubid: 121221


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Institutionen för matematiska vetenskaper, matematik (2005-2016)


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Chalmers infrastruktur