Hi, another diff. eq problem:
In my notes, it suggests to use a similarity transformation to solve the heat equation in one dimension .
So if and , then:
...What?
any help in explaining this would be much appreciated.
Hi, another diff. eq problem:
In my notes, it suggests to use a similarity transformation to solve the heat equation in one dimension .
So if and , then:
...What?
any help in explaining this would be much appreciated.
You have . Letting then then:
and:
ok, you do in terms of partial of v with respect to . When I do that and simplify, I get:
Solving that and converting back to x and t, I get an answer in terms of the exponential integral which, when I back-substitute, satisfies the PDE.