Subject:PARTIAL DIFFERENTIAL EQUATION At the top there is equation (1) which u will use in part (a) of given question. Kindly use Use Cauchy characteristic method yo solve this full question(i.e part a&b) . Kindly solve this as soon as possible THANK YOU u(r + ht,+,k) + u(x- h, t k)=u(x+ k, t+h) + u(x – k,t – h), ....eq()This is equation (1) whichcharacteristic methodQ.Consider the initial boundary value problems:x € (0, 7), t> 0,Ofu – 0u = 0,u(x, 0) = 0,x € (0, 7), initial data,t > 0, boundary values.dru(x, 0) = 1,%3Du(T, t) = 0,%3Du(0, t) = 0,%3D(a) Solve it using formula (1).(b) Is the resulting solution continuous? Is C' i.e, u(x, t) differentiablewith du(x, t), d„u(x, t) continuous?Use Cauchy

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Answered: PARTIAL DIFFERENTIAL EQUATION At the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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Subject:PARTIAL DIFFERENTIAL EQUATION At the top there is equation (1) which u will use in part (a) of given question. Kindly use Use Cauchy characteristic method yo solve this full question(i.e part a&b) . Kindly solve this as soon as possible THANK YOU

u(r + ht,+,k) + u(x- h, t k)=u(x+ k, t+h) + u(x – k,t – h), ....eq()
This is equation (1) which
characteristic method
Q.
Consider the initial boundary value problems:
x € (0, 7), t> 0,
Ofu – 0u = 0,
u(x, 0) = 0,
x € (0, 7), initial data,
t > 0, boundary values.
dru(x, 0) = 1,
%3D
u(T, t) = 0,
%3D
u(0, t) = 0,
%3D
(a) Solve it using formula (1).
(b) Is the resulting solution continuous? Is C' i.e, u(x, t) differentiable
with du(x, t), d„u(x, t) continuous?
Use Cauchy

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