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Question: PDETools:-dchange example

Question:PDETools:-dchange example

Rouben Rostamian 8721 Maple 2024
pdetools dchange
5 hours ago
2

In the following example, the result of PDETools:-dchange()  is unexpected.  This may be due to my misunderstanding of the documentation, or (hopefully not) a bug.  Any comments?

> 

restart;
> 

with(PDETools):

Differential equation over 0 < x and x < 5:

> 

de := diff(u(x),x) + x*u(x) = 0;

diff(u(x), x)+x*u(x) = 0

Transform the domain from 0 < x and x < 5 to 0 < xi and xi < 1:

> 

tr := x = 5*xi,  u(x) = v(xi);

x = 5*xi, u(x) = v(xi)

> 

dchange({tr}, de, {xi, v(xi)});

(1/5)*(diff(v(xi), xi))+5*xi*v(xi) = 0

That's good.  Now do the same thing to a generic first order ODE:

> 

DE := F(x,u(x),diff(u(x),x));

F(x, u(x), diff(u(x), x))

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dchange({tr}, DE, {xi, v(xi)});

F(xi, v(xi), (1/5)*(diff(v(xi), xi)))

That's not good.  The first argument of "F," which was x, should have changed to 5*xi.

> 

 

Download dchange-problem.mw

 
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