Consider the equation ut = uxx, 0 < x < 1, t > 0, with boundary condition u(0, t) = -4, u(1, t)

Step 1: Find the steady state solution (U_{steady state}(x)) by solving for the constants (a) an

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Consider the equation u_t = u_xx, 0 < x < 1, t > 0, with boundary condition u(0, t) = -4, u(1, t) = 3, and initial condition u(x, 0) = e^x. Setup we wish to change the problem into homogeneous boundary conditions. What is the steady state solution: u_steady state(x) = Let U(x, t) denote the transient solution. That is, the solution of U_t = U_xx, 0 < x < 1, t > 0, with boundary condition U(0, t) = 0, U(1, t) = 0, and initial condition U(x, 0) = where the initial condition is such that u(x, t) = u_steady state(x) + U(x, t) solves the original problem above.

          Consider the equation u_t = u_xx, 0 < x < 1, t > 0, with boundary condition u(0, t) = -4, u(1, t) = 3, and initial condition u(x, 0) = e^x.
Setup we wish to change the problem into homogeneous boundary conditions. What is the steady state solution:
u_steady state(x) =
Let U(x, t) denote the transient solution. That is, the solution of U_t = U_xx, 0 < x < 1, t > 0, with boundary condition U(0, t) = 0, U(1, t) = 0, and initial condition
U(x, 0) =
where the initial condition is such that
u(x, t) = u_steady state(x) + U(x, t)
solves the original problem above.

Consider the equation ut = uxx, 0 < x < 1, t > 0, with boundary condition u(0, t) = -4, u(1, t) = 3, and initial condition u(x, 0) = e^x.
Setup we wish to change the problem into homogeneous boundary conditions. What is the steady state solution:
usteady state(x) =
Let U(x, t) denote the transient solution. That is, the solution of Ut = Uxx, 0 < x < 1, t > 0, with boundary condition U(0, t) = 0, U(1, t) = 0, and initial condition
U(x, 0) =
where the initial condition is such that
u(x, t) = usteady state(x) + U(x, t)
solves the original problem above.

Added by Jillian H.

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