Question

In: Advanced Math

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).

Solutions

Expert Solution


Related 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 < 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
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
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
Derive a finite-difference method for solving the non-linear parabolic equation using the Explicit Method Ut=v*Uxx-U*Ux Where...
Derive a finite-difference method for solving the non-linear parabolic equation using the Explicit Method Ut=v*Uxx-U*Ux Where v is the viscosity
Derive a finite-difference method for solving the non-linear parabolic equation using the Explicit Method Ut=v*Uxx-U*Ux Where...
Derive a finite-difference method for solving the non-linear parabolic equation using the Explicit Method Ut=v*Uxx-U*Ux Where v is the viscosity
Consider the discrete-time LTI system characterized by the following difference equation with input and initial conditions specified
  Consider the discrete-time LTI system characterized by the following difference equation with input and initial conditions specified: y[n] - 2 y[n-1] – 3 y[n-2] = x[n] , with y[0] = -1 and y[1] = 0, x[n] = (-1/2)n u[n-2]. ? Write a MATLAB program to simulate this difference equation. You may try the commands ‘filter’ or ‘filtic’ or create a loop to compute the values recursively. ? Printout and plot the values of the input signal, x[n] and the...
Consider the time series Xt = 4t + Wt + 0.9Wt−1, where Wt ∼ N(0, σ2...
Consider the time series Xt = 4t + Wt + 0.9Wt−1, where Wt ∼ N(0, σ2 ). (i)What are the mean function and the variance function of this time series? Is this time series stationary? Justify your answer (ii). Consider the first differences of the time series above, that is, consider Yt = Xt − Xt−1. What are the mean function and autocovariance function of this time series? Is this time series stationary? Justify your answer
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)
(a) Consider the temperature dependent heat capacity of O2(g) given in the Resource section of your...
(a) Consider the temperature dependent heat capacity of O2(g) given in the Resource section of your textbook (29.355J/Kmol). What is the heat absorbed at constant pressure when 1 mole of O2(g) is heated from 0o C to 500oC? (Hint: Integrate!) (b) Construct a plot of Cp,m (for O2(g)) vs. T and plot it between 0 and 500 oC. What is the % error if you had used a temperature-independent heat capacity for part (a)?
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT