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**Harvard**

McLean, W. och Thomée, V. (2010) *NUMERICAL SOLUTION VIA LAPLACE TRANSFORMS OF A FRACTIONAL ORDER EVOLUTION EQUATION*.

** BibTeX **

@article{

McLean2010,

author={McLean, W. and Thomée, Vidar},

title={NUMERICAL SOLUTION VIA LAPLACE TRANSFORMS OF A FRACTIONAL ORDER EVOLUTION EQUATION},

journal={Journal of Integral Equations and Applications},

issn={0897-3962},

volume={22},

issue={1},

pages={57-94},

abstract={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.},

year={2010},

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

}

** RefWorks **

RT Journal Article

SR Electronic

ID 121221

A1 McLean, W.

A1 Thomée, Vidar

T1 NUMERICAL SOLUTION VIA LAPLACE TRANSFORMS OF A FRACTIONAL ORDER EVOLUTION EQUATION

YR 2010

JF Journal of Integral Equations and Applications

SN 0897-3962

VO 22

IS 1

SP 57

OP 94

AB 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.

LA eng

DO 10.1216/JIE-2010-22-1-57

LK http://dx.doi.org/10.1216/JIE-2010-22-1-57

OL 30