Consider the following PDE: Let us introduce new variables (, n) defined by Using the chain rule, rewrite the PDE in terms of u(§, n) = u(z(§, n), t(§, n)) and its derivatives: Uzz 5U + 2u₂ + 4u₂ = 0 9 = 2+ 3t and 7=z-3t

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Consider the following PDE:
Let us introduce new variables (, n) defined by
Using the chain rule, rewrite the PDE in terms of u(, n) = u(x(§, n), t(§, 7)) and its derivatives:
UII
Check
Utt
New PDE:
U EE +
un +
Warning: Please do not try to divide both side of the PDE by a constant in order to simplify it. The computer will consider it as a wrong answer...
Um +
+2uz +4ut = 0
= x + 3t and n = x - 3t
Uε +
U11
=
0
Transcribed Image Text:Consider the following PDE: Let us introduce new variables (, n) defined by Using the chain rule, rewrite the PDE in terms of u(, n) = u(x(§, n), t(§, 7)) and its derivatives: UII Check Utt New PDE: U EE + un + Warning: Please do not try to divide both side of the PDE by a constant in order to simplify it. The computer will consider it as a wrong answer... Um + +2uz +4ut = 0 = x + 3t and n = x - 3t Uε + U11 = 0
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