Runge Kutta Chebyshev Method for parabolic ... - Brown University
Runge Kutta Chebyshev Method for parabolic ... - Brown University
Runge Kutta Chebyshev Method for parabolic ... - Brown University
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Introduction Properties Pros and Cons Examples References<br />
Eg 2: combustion problem<br />
ct = ∆c−Dce −δ/T , LTt = ∆T+αDce −δ/T , 0 < x, y, z < 1, 0 � t � 0.3<br />
(48)<br />
L = 0.9, α = 1, δ = 20, D = Re δ /αδ, with R = 5<br />
The grid spacing is h = 1/(N + 0.5), with N = 40,<br />
2 × 40 3 = 128000 equations<br />
Tol maxError #steps #F-evals CPU(s)<br />
RKC BDF RKC BDF RKC BDF RKC BDF<br />
1.E-4 5.4E-1 8.7E-1 51 33 525 285 420 412<br />
1.E-5 1.8E-1 7.6E-1 124 91 781 659 630 957<br />
1.E-6 3.9E-2 1.2E-1 270 201 1270 1141 1030 1702<br />
1.E-7 8.7E-3 1.2E-3 581 286 2147 1548 1758 2376<br />
The low accuracy is expected from the local instability of the<br />
problem.
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