Mathematics Homework Solutions
#39038
Partial Differential Equation : Diffusion Equation and Explicit Series Solution
Consider the diffusion equation
ut = ku.xx for 0 < < pi and t > 0 with the boundary conditions
ux(0, t) = 0 and u(pi, t) = 0
and the initial condition
u(x,0) = 1.
(a) Find the separated solutions satisfying the differential equation and boundary conditions.
(b) Use these solutions to write an explicit series solution to the differential equation satisfying the boundary conditions and the initial condition.
A Diffusion Equation and Explicit Series Solution are investigated. The solution is detailed and well presented. The response was given a rating of "5" by the student who originally posted the question.
What is this?
By OTA - Overall OTA Rating
Changping Wang, MA - 4.9/5
Purchase Cost Now
$2.19 CAD (was ~$7.98)
Included in Download
- Plain text response
- Attached file(s):
- 4-1.doc
Why you can trust BrainMass.com
- Your Information is Secure
- Best Online Academic Help Service
- Students find real academic Success
- Diffusion Equation - Show that S(x,y,t)=S(x,t)S(y,t) satisfies the diffusion equation. S_t = k(S_xx + S_yy)
- Diffusion Equation : Energy Decreasing as a Function of Time - 3. Suppose that u(x. t) satisfies the diffusion equation ut = kuxx for 0 < x < L and t > 0, and the Robin boundary conditions ux(0, t) - aou(0, t) = 0 and ux(L, t) + aLu(L, t) = 0 where k, L, a0 an ...
- Diffusion - Hello, I have a test coming up soon and I don't understand how to solve the kind of problem as given below. Please provide some explanation in the solution. Thanks in advance, Eriko
- Diffusion Equation : Compute the first three 'lines' U j,k's : the nine values U1,1 through U3,3 - Please see the attached file for the fully formatted problems.
- One dimentional unsteady diffusion - (See attached file for full problem description) 5.7 a) Consider one-dimensional unsteady diffusion in an absorbing medium. The causal fundamental solution E with pole at x = 0, t=0 satisfies R ...
