Question
In: Advanced Math
Solve the following heat equation using Fourier Series uxx = ut, 0 < x < pi,...
Solve the following heat equation using Fourier Series
uxx = ut, 0 < x < pi, t > 0, u(0,t) = 0 = u(pi,t), u(x,0) = sinx - sin3x
Solutions
Colby Messinger answered 2 years agoRelated Solutions
Solve the following heat equation using Fourier Series uxx = ut, 0 < x < 1,...
Solve the following heat equation using Fourier Series
uxx = ut, 0 < x < 1, t > 0,
u(0,t) = 0 = u(1,t), u(x,0) = x/2
Solve the following heat equation using Fourier Series uxx = ut, 0 < x < 1,...
Solve the following heat equation using Fourier Series
uxx = ut, 0 < x < 1, t > 0,
ux(0,t) = 0 = ux(1,t), u(x,0) = 1 -
x2
Solve the following wave equation using Fourier Series a2uxx = utt, 0 < x < pi,...
Solve the following wave equation using Fourier Series
a2uxx = utt, 0 < x < pi,
t > 0, u(0,t) = 0 = u(pi,t), u(x,0) = sinx, ut(x,0) =
pi - x
Solve the following wave equation using Fourier Series a2uxx = utt, 0 < x < 1,...
Solve the following wave equation using Fourier Series
a2uxx = utt, 0 < x < 1, t
> 0, u(0,t) = 0 = u(1,t), u(x,0) = x2,
ut(x,0) = 0
Solve the nonhomogeneous heat equation: ut-kuxx=sinx, 0<x<pi, t>0 u(0,t)=u(pi,t)=0, t>0 u(x,0)=0, 0<x<pi
Solve the nonhomogeneous heat equation:
ut-kuxx=sinx, 0<x<pi, t>0
u(0,t)=u(pi,t)=0, t>0
u(x,0)=0, 0<x<pi
Consider the equation utt = uxx x ∈ (0, pi) ux(0,t) = u(pi,t) = 0 Write...
Consider the equation utt = uxx
x ∈ (0, pi)
ux(0,t) = u(pi,t) = 0
Write the series expansion for a solution u(x,t)
Find the finite-difference solution of the heat-conduction problem PDE: ut = uxx 0 < x <...
Find the finite-difference solution of the heat-conduction
problem
PDE: ut = uxx 0 < x < 1, 0 < t < 1
BCs:
⇢
u(0, t) = 0
ux(1, t) = 0
0 < t < 1
IC: u(x, 0) = sin(pi x) 0 x 1
for t = 0.005, 0.010, 0.015 by the explicit method. Assume
Using the method of separation of variables and Fourier series, solve the following heat conduction problem...
Using the method of separation of variables and Fourier series,
solve the following heat
conduction problem in a rod.
∂u/∂t =∂2u/∂x2
, u(0, t) = 0, u(π, t) = 3π, u(x, 0) = 0
Consider the nonhomogenous heat equation with time dependent sources ut = uxx + xt, an initial...
Consider the nonhomogenous heat equation with time dependent
sources ut = uxx + xt, an initial condition
u(x, 0) = x2 and inhomogenous boundary conditions
ux(0, t) = 2t and ux(1, t) = 4. Use eigen
function expansion to find the solution u(x, t).
Please solve the following: ut=uxx, 0<x<1, t>0 u(0,t)=0, u(1,t)=A, t>0 u(x,0)=cosx, 0<x<1
Please solve the following:
ut=uxx, 0<x<1, t>0
u(0,t)=0, u(1,t)=A, t>0
u(x,0)=cosx, 0<x<1
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