I have this partial differential equation
http://en.wikipedia.org/wiki/Burgers%27_equation
To which I want to substitute an ansatz that depends just on one variable:
f(xi), where xi is a function of the two independent variables x and t.
After the substitution, I would like to isolate the derivative d(f)/d(xi).
I tried writing a script to do it, but I can't refer to the relevant
derivative.
Attached herein is the script. Here's the output I get:
(-nu*xi**3*Subs(Derivative(f(_xi_1), _xi_1), (_xi_1,), (xi,))/2 -
nu*xi**2*Subs(Derivative(f(_xi_1), _xi_1, _xi_1), (_xi_1,), (xi,)) +
2*nu*xi*Subs(Derivative(f(_xi_1), _xi_1), (_xi_1,), (xi,)) - 2*nu*f(xi) +
xi*f(xi)*Subs(Derivative(f(_xi_1), _xi_1), (_xi_1,), (xi,)) -
f(xi)**2)/(xi**3*(nu*t)**(3/2))
[]
None
Any help will be welcome.
- Almog
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def burgers(f,x,t, nu):
import sympy
return sympy.diff(f,t)+f*sympy.diff(f,x)-nu*sympy.diff(f,x,2)
def main():
import sympy
x, t, nu, xi = sympy.var('x, t, nu, xi')
f = sympy.Function('f')
temp = burgers(f(x/sympy.sqrt(nu*t))/x,x,t,nu)
temp = temp.subs(x,xi*sympy.sqrt(nu*t))
temp = sympy.simplify(temp)
print temp
print sympy.solve(temp,sympy.diff(f(xi),xi))
wc = sympy.Wild('wc')
print temp.match(sympy.diff(f(wc),wc))
if __name__ == '__main__':
main()
