Two identical very long rods are at different temperatures T| and T2. At time t = 0[ they are attached; then, the system will satisfy the problem u – kurz = 0, – 0 < x < 00, t> 0 (T1, if æ < 0 u(x,0) = T2, if x > 0 The solution is u(x, t) = Write your solution in terms of the error function erf and complementary error function erfd, and use "T1" and "T2" in the place of T|| and T, respectively. Hint: The error function is defined by erf(x) = =. e and the complementary error function is defined by 2 erfc(x) = 1 – erf(æ) =
Two identical very long rods are at different temperatures T| and T2. At time t = 0[ they are attached; then, the system will satisfy the problem u – kurz = 0, – 0 < x < 00, t> 0 (T1, if æ < 0 u(x,0) = T2, if x > 0 The solution is u(x, t) = Write your solution in terms of the error function erf and complementary error function erfd, and use "T1" and "T2" in the place of T|| and T, respectively. Hint: The error function is defined by erf(x) = =. e and the complementary error function is defined by 2 erfc(x) = 1 – erf(æ) =
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Two identical very long rods are at different temperatures T||and T2. At time t = 0l they are attached; then, the system will satisfy the problem
Ut – k*uzz = 0, – 0 < x < 0, t > 0
S T1,
if x < 0
u(x, 0)
T2,
if x >0
The solution is
u(x, t) =
Write your solution in terms of the error function erf and complementary error function erfd, and use "T1"and "T2" in the place of T| and T, respectively.
Hint: The error function is defined by
erf(x)
e
and the complementary error function is defined by
erfc(x) = 1 – erf(x)
dt
e
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