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Question: Saddle point of a 2 variable complex function

Question:Saddle point of a 2 variable complex function

milver 12 Maple
calculus fsolve saddle-point
March 11 2009
0

I am trying to solve the following function for 'r' and 'theta' at various values of 'a' and 'zeta' in order to detemine the saddle points (r,theta). I have tried the following and it works fine! However, the process takes quite a long time. I was wondering if there is another method...say Newtons Method or otherwise to go about solving the two simultaneous equations (eq1,eq2) for (r,theta)?

Thanks

Robert

a:=1: zeta:=1:

f:= (a,zeta,r,theta) -> -exp(I*zeta/(1 - exp(-r*exp(I*theta)))) * r * exp(I*(a*r*exp(I*theta) + theta))/(2*Pi*(1 - exp(r*exp(I*theta))));

absf:=evalc(conjugate(f(a,zeta,r,theta))*f(a,zeta,r,theta)):

eq1:=diff(absf,r):

eq2:=diff(absf,theta):

assume(r>0,theta>0):

fsolve({eq1=0,eq2=0},{r,theta});
Please Wait...