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    1D heat equation with non-homogenous boundary conditions

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    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.

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    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.