File: convect-1d.mac

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assume(u>0);
assume(t>0);
assume(x>0);
x0:u*t;
ffunction;
/*
le choix de lambda n'interfere pas sur le residu:
lambda: a*nu/t0;
*/
r : -1/(4*nu*t+t0);
depends(r,t);
phi:exp( - lambda*t + r*(x-x0)**2);
residue;
res:   diff(phi,t)
  +  u*diff(phi,x)
  - nu*diff(diff(phi,x),x)
  + (lambda + 2*r*nu)*phi
$
res:factor(trigsimp(res/((x-x0)*phi)))$
res;
/*
ssssssssss;
ode2(res=0,r,t);
*/