Re: change of variables

*To*: mathgroup at smc.vnet.net*Subject*: [mg71265] Re: change of variables*From*: bghiggins at ucdavis.edu*Date*: Sun, 12 Nov 2006 06:48:11 -0500 (EST)*References*: <ej4352$r9c$1@smc.vnet.net>

You can try the following approach: Let suppose you have the 1-D heat equation where the dimensional temperature v is a function of time(t) and the spatial coordinate (x). Here is the equation where K is the thermal diffusivity heatEqn := D[v[x, t], t] == K D[v[x, t], {x, 2}] Now let us introduce the following dimensionless varaibles bases on a temperature scale V, a length scale L , and a time scale T Î·[x_] := x/L Ï?[t_] := t/T v[x, t] := Ï?[Î·[x], Ï?[t]]/Î¦ Then evaluating In[5]:= heatEqn /. {x/L -> Î·, t/T -> Ï?} Out[5]= Derivative[0, 1][Ï?][Î·, Ï?]/(T*Î¦) == (K*Derivative[2, 0][Ï?][Î·, Ï?])/(L^2*Î¦) One can apply additional rules to simplify the resulting dimensionless equation if needed. Hope this helps, Cheers Brian hussain.alqahtani at gmail.com wrote: > Dear Members, > > I have a differential equation that i need to nondimensionalize. > Therefore, i introduced a new nondimensional varibles and so that i get > a nondimensional equation. I am wondering how can i do that in > Mathematica?. For example if i have this term: > > K*D[v,{x,2}], > > my new nondimensional variables are: > > x*=x/L and v*=v/L, > > I can do that by hand, but since i have a huge number of equations, i > rather prefer to use Mathematica. > > I appreciate any help in this regard, and many thanks in anticipation. > > HMQ