Let u (x, t) defined for a e [0, 1] and t 20 such that Ut = Uxx for t>0, 0< x < 1, (2.7) u(0, t) = u(1, t) = 0 for t> 0, (2.8) u(x,0) = u°(x), for 0

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Let u (x, t) defined for x e [0, 1] and t 20 such that
Ut = Uxx for t>0, 0< a < 1,
(2.7)
u(0, t) = u(1, t) = 0 for t> 0,
(2.8)
u(x,0) = u°(x), for 0<x < 1.
(2.9)
where
2x
u°(x) =
if 0<x <},
2 – 2x if < < 1.
(a) Conduct one time step to approximate u (x, t) using an explicit difference scheme with:
1. J = 20 (Ax = 0.05) and At = 0.0012
2. J = 20 (Ax = 0.05) and At = 0.0013
Transcribed Image Text:Let u (x, t) defined for x e [0, 1] and t 20 such that Ut = Uxx for t>0, 0< a < 1, (2.7) u(0, t) = u(1, t) = 0 for t> 0, (2.8) u(x,0) = u°(x), for 0<x < 1. (2.9) where 2x u°(x) = if 0<x <}, 2 – 2x if < < 1. (a) Conduct one time step to approximate u (x, t) using an explicit difference scheme with: 1. J = 20 (Ax = 0.05) and At = 0.0012 2. J = 20 (Ax = 0.05) and At = 0.0013
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