f. dubois - Laboratoire de Mathématiques et de leurs Applications ...
f. dubois - Laboratoire de Mathématiques et de leurs Applications ...
f. dubois - Laboratoire de Mathématiques et de leurs Applications ...
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Intro Racines carrées Collocation mixte Tests numériques Joulin Chaleur Couplage Couplage simplifié<br />
Premiers tests numériques (xvi)<br />
• Comparison with published results :<br />
previous numerical algorithms proposed by<br />
Lubich (1986), Blank (1996), Di<strong>et</strong>helm (1997),<br />
Di<strong>et</strong>helm and Ford (1999), Di<strong>et</strong>helm and Luchko (2000).<br />
• Example of test case proposed by L. Blank (1996) :<br />
D 1/2 u + u = 0, t > 0<br />
u = 1, t ≤ 0.<br />
• Analytical solution : u (t) = e t 1 − erf √ t .<br />
A particular case of the Mittag-Leffler exponential :<br />
Eα(θ) =<br />
∞<br />
k=0<br />
(23)<br />
θk . (24)<br />
Γ(1 + α k)
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