Let u be the solution to the initial boundary value problem for the Heat Equation, du(t, x) = 3 du(t, x), t≤ (0, ∞), x = (0,1); with Mixed boundary conditions du(t,0) = 0 and u(t, 1) = 0 and with initial condition € [0₁-1½)₁ = [1,1]. The solution u of the problem above, with the conventions given in class, has the form with the normalization conditions vn (0) vn (t) = wn(x) = Cn = u(0, x) = f(x) = = 1 and wn (0) 5, = 0, x 0, u(t, x) = Σ en vn (t) wn(x), n=1 x = 1. Find the functions vn, wn, and the constants Cn. Σ M M
Let u be the solution to the initial boundary value problem for the Heat Equation, du(t, x) = 3 du(t, x), t≤ (0, ∞), x = (0,1); with Mixed boundary conditions du(t,0) = 0 and u(t, 1) = 0 and with initial condition € [0₁-1½)₁ = [1,1]. The solution u of the problem above, with the conventions given in class, has the form with the normalization conditions vn (0) vn (t) = wn(x) = Cn = u(0, x) = f(x) = = 1 and wn (0) 5, = 0, x 0, u(t, x) = Σ en vn (t) wn(x), n=1 x = 1. Find the functions vn, wn, and the constants Cn. Σ M M
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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![Let u be the solution to the initial boundary value problem for the Heat Equation,
du(t, x) = 3 du(t, x), t≤ (0, ∞), x = (0,1);
with Mixed boundary conditions du(t,0) = 0 and u(t, 1) = 0 and with initial condition
€ [0₁-1½)₁
= [1,1].
The solution u of the problem above, with the conventions given in class, has the form
with the normalization conditions vn (0)
vn (t) =
wn(x) =
Cn =
u(0, x) = f(x) =
=
1 and wn (0)
5,
=
0,
x 0,
u(t, x) = Σ en vn (t) wn(x),
n=1
x =
1. Find the functions vn, wn, and the constants Cn.
Σ
M
M](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0695e04c-6177-4dae-ae8e-62e62853c8ae%2Fc062e23e-d1b3-4b04-9422-d1c52673832f%2F34hwhub_processed.png&w=3840&q=75)
Transcribed Image Text:Let u be the solution to the initial boundary value problem for the Heat Equation,
du(t, x) = 3 du(t, x), t≤ (0, ∞), x = (0,1);
with Mixed boundary conditions du(t,0) = 0 and u(t, 1) = 0 and with initial condition
€ [0₁-1½)₁
= [1,1].
The solution u of the problem above, with the conventions given in class, has the form
with the normalization conditions vn (0)
vn (t) =
wn(x) =
Cn =
u(0, x) = f(x) =
=
1 and wn (0)
5,
=
0,
x 0,
u(t, x) = Σ en vn (t) wn(x),
n=1
x =
1. Find the functions vn, wn, and the constants Cn.
Σ
M
M
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