Let a 3 and 3 = 7 throughout this question. (i) Using seperation of variables, solve the heat equation DU 8²U Ət əx² for a function U(x, t) in the range x € [0, 1] and t€ [0, ∞) together with the boundary conditions U(x=0, t) = 0, U (x = 1,t) = 0, and the initial condition U(x, t0) = { (1-x) 0≤x≤ ¹ (1-x) ≤x≤i
Let a 3 and 3 = 7 throughout this question. (i) Using seperation of variables, solve the heat equation DU 8²U Ət əx² for a function U(x, t) in the range x € [0, 1] and t€ [0, ∞) together with the boundary conditions U(x=0, t) = 0, U (x = 1,t) = 0, and the initial condition U(x, t0) = { (1-x) 0≤x≤ ¹ (1-x) ≤x≤i
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
H3.
![Let a =
3 and 37 throughout this question.
(i) Using seperation of variables, solve the heat equation
au
J²U
Ət
əx²
for a function U(x, t) in the range x = [0, 1] and t = [0, ∞) together with the boundary
conditions
U(x=0, t) = 0,
U(x = 1,t) = 0,
and the initial condition
U(x, t0) =
S Bx
(ii) If the error function is defined as
Show all your working.
(1-x)
0≤x≤ 1/2
≤x≤i
erf(2)=√₁
re-express the following integral in terms of the error function
Lov
e-²
dy,
-x²+x-³ dx.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffd0ad285-993a-4693-bd2d-c219acf44c8e%2Fb1325e79-9f04-41d8-acdc-efa2ad37374d%2Frjgc2g_processed.png&w=3840&q=75)
Transcribed Image Text:Let a =
3 and 37 throughout this question.
(i) Using seperation of variables, solve the heat equation
au
J²U
Ət
əx²
for a function U(x, t) in the range x = [0, 1] and t = [0, ∞) together with the boundary
conditions
U(x=0, t) = 0,
U(x = 1,t) = 0,
and the initial condition
U(x, t0) =
S Bx
(ii) If the error function is defined as
Show all your working.
(1-x)
0≤x≤ 1/2
≤x≤i
erf(2)=√₁
re-express the following integral in terms of the error function
Lov
e-²
dy,
-x²+x-³ dx.
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