Question

Using separation of variables to solve the heat equation, ut = kuxx on the interval 0...

  1. Using separation of variables to solve the heat equation, ut = kuxx on the interval 0 < x < 1 with boundary conditions ux (0, t ) = 0 and ux (1, t ) = 0, yields the general solution,

    ∞
    u(x,t) = A0 + ?Ane−kλnt cos?nπx? (with λn = n2π2)

n=1DeterminethecoefficientsAn(n=0,1,2,...)whenu(x,0)=f(x)= 0, 1/2≤x<1 .

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Solve heat equation for the following conditions ut = kuxx t > 0, 0 < x...
Solve heat equation for the following conditions ut = kuxx t > 0, 0 < x < ∞ u|t=0 = g(x) ux|x=0 = h(t) 2. g(x) = 1 if x < 1 and 0 if x ≥ 1 h(t) = 0; for k = 1/2
1. Solve fully the heat equation problem: ut = 5uxx u(0, t) = u(1, t) =...
1. Solve fully the heat equation problem: ut = 5uxx u(0, t) = u(1, t) = 0 u(x, 0) = x − x ^3 (Provide all the details of separation of variables as well as the needed Fourier expansions.)
Solve the heat equation and find the steady state solution: uxx = ut, 0 < x...
Solve the heat equation and find the steady state solution: uxx = ut, 0 < x < 1, t > 0, u(0,t) = T1, u(1,t) = T2, where T1 and T2 are distinct constants, and u(x,0) = 0
Solve the below boundary value equation 1. Ut=2uxx o<x<pi 0<t 2. u(0,t) = ux(pi,t) 0<t 3....
Solve the below boundary value equation 1. Ut=2uxx o<x<pi 0<t 2. u(0,t) = ux(pi,t) 0<t 3. u(x,0) = 1-2x 0<x<pi
Solve the heat equation ut = k uxx, 0 < x < L, t > 0...
Solve the heat equation ut = k uxx, 0 < x < L, t > 0 u(0, t) = u(L, t) = 0, t > 0 u(x, 0) = f(x), 0 < x < L a) f(x) = 6 sin 9πx L b) f(x) = 1 if 0 < x ≤ L/2 2 if L/2 < x < L
uxx = ut - u (0<x<1, t>0), boundary conditions: u(1,t)=cost, u(0,t)= 0 initial conditions: u(x,0)= x...
uxx = ut - u (0<x<1, t>0), boundary conditions: u(1,t)=cost, u(0,t)= 0 initial conditions: u(x,0)= x i) solve this problem by using the method of separation of variables. (Please, share the solution step by step) ii) graphically present two terms(binomial) solutions for u(x,1).
In each of Problems 1 through 8, find the steady-state solution of the heat conduction equation...
In each of Problems 1 through 8, find the steady-state solution of the heat conduction equation α2uxx = ut that satisfies the given set of boundary conditions. 1. ux (0, t) = 0, u( L, t) = 0 2. u(0, t) = 0, ux ( L, t) = 0
Can you please solve this question, Using separation of variables, write down a complete list of...
Can you please solve this question, Using separation of variables, write down a complete list of L^2 eigenfunctions and of eigenvalues for the Laplacian on the cylinder D X [-1, 1], with homogeneous Dirichlet boundary conditions, where D is the (two-dimensional) disk centered at the origin of radius 2. b) Use this to solve the heat equation partial u / partial t = Delta u on this cylinder with homogeneous Dirichlet boundary conditions, with initial data u(x, y, z, 0)...
Solve the heat equation and find the steady state solution : uxx=ut 0<x<1, t>0, u(0,t)=T1, u(1,t)=T2,...
Solve the heat equation and find the steady state solution : uxx=ut 0<x<1, t>0, u(0,t)=T1, u(1,t)=T2, where T1 and T2 are distinct constants, and u(x,0)=0
Use the Fourier sine transform to derive the solution formula for the heat equation ut =...
Use the Fourier sine transform to derive the solution formula for the heat equation ut = c2 uxx on the half-infinite bar (0 ≤ x < ∞) with Dirichlet boundary condition u(0, t) = a, for some constant a, and initial condition u(x, 0) = f(x).
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT