Transform the problem

PDE:\quad u_{t} = 9 u_{xx} , \qquad 0 < x < 6 , \quad t > 0

BC:\quad u(0,t) = 8 \quad u(6,t) = 9

IC:\quad u(x,0) = x^2

into a dimensionless problem:

PDE:\quad U_{\tau} = U_{\xi\xi} , \qquad 0 < \xi < 1 , \quad \tau > 0

BC:\quad U(0,\tau) = 0 \quad u(1,\tau) = 1

IC:\quad U(\xi,0) = {}

Type xi, tau for the variables.

First, you transform u to U. Use just small "u" instead of "u(x,t)":

U = {}

Next, transformx to \xi .

\xi = {}

Finally, transformt to \tau .

\tau = {}

help (formulas)

PDE:

BC:

IC:

into a dimensionless problem:

PDE:

BC:

IC:

Type xi, tau for the variables.

First, you transform u to U. Use just small "u" instead of "u(x,t)":

Next, transform

Finally, transform

help (formulas)

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