Solve the following heat equation using Fourier Series uxx = ut, 0 < x < pi,...

Solve the following heat equation using Fourier Series

u_xx = u_t, 0 < x < pi, t > 0, u(0,t) = 0 = u(pi,t), u(x,0) = sinx - sin3x

Expert Solution

Colby Messinger answered 2 years ago

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

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

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)

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

Question

Solve the following heat equation using Fourier Series uxx = ut, 0 < x < pi,...

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,...

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 < 1,...

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

Find the finite-difference solution of the heat-conduction problem PDE: ut = uxx 0 < x <...

Consider the equation utt = uxx x ∈ (0, pi) ux(0,t) = u(pi,t) = 0 Write...

Using the method of separation of variables and Fourier series, solve the following heat conduction problem...

Consider the nonhomogenous heat equation with time dependent sources ut = uxx + xt, an initial...

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