Hi,(adsbygoogle = window.adsbygoogle || []).push({});

I have to change the variable in the following eqn, although I know the answer I cannot see how the answer was arrived at:

We start with a p.d.e in F(S,t)

-dF = -rF + (r- delta)SdF+0.5(theta^2)(S^2)d^2F

dt dS dS^2

We then want to change to X=1/S F(S,t)=Sf(X,t)

The answer is:

-df = -deltaf + (delta- r)Sdf+0.5(theta^2)(S^2)d^2f

dt dS dS^2

Now the way I see it:

-dF = -Sdf part 1

dt dt

-rF = -r.S.f not sure how this becomes delta? part 2

(r-delta)SdF=(r-delta)S^2df. dX=(delta-r)S^2df . 1

dS dX dS dX S^2

=(delta-r)df .1 (when you divide through with the S from part 1)

dX S

=(delta-r)df. X part 3

dX

Lastly

.5(theta^2)S^2d^2F=.5(theta^2)S^3d^2 .dX^2

dS^2 dX^2 dS^2

=(.5*theta^2).S^3.d^2f . -2

dX^2 X^3

=theta^2.d^2f .X where the .X comes from dividing through by S from part 1

dX^2

= part 4

Part 4 clearly is wrong but I'm not sure where I've made the mistake?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Change of Variable

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**