Explore BrainMass
Share

Explore BrainMass

    1D heat equation with non-homogenous boundary conditions

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    Please see the attached file for the fully formatted problem.

    Solve the heat equation

    u_t =a^2 * u_xx

    for 0<x<L

    under the conditions:
    u(0,t)=1 u(L,t)=2 u(x,0)=0

    Solve this problem by converting this problem into a problem with homogeneous boundary conditions. Show that as t approaches infinity the solution approaches the equilibrium solution.

    © BrainMass Inc. brainmass.com October 9, 2019, 11:03 pm ad1c9bdddf
    https://brainmass.com/math/algebra/heat-equation-nonhomogenous-boundary-conditions-242476

    Attachments

    Solution Summary

    The solution shows in full details how to convert the problem to a solvable homogeneous problem, solves it and then shows how it behaves at a steady state.

    $2.19