Hello,
I am using Mathematica to solve a set of equations and it keeps
showing a error message "FindRoot::jsing: Encountered a singular
Jacobian at the point {A1,A2,A3,Ea1,Ea2,Ea3} =
{-2629.39,758889.,4.12521*10^6,-19229.4,-21903.5,-71770.6}. Try
perturbing the initial point(s). >>".
The equations that I am trying to solve is :
-----------------------------------------------------------------------------------------------------------------------------------------------------------
FindRoot[{A1*Exp[Ea1/(8.314*(48 + 273.15))] +
A2*Exp[ Ea2/(8.314*(48 + 273.15))] +
A3*Exp[Ea3/(8.314*(48 + 273.15))] == 0.0183,
A1*Exp[Ea1/(8.314*(44 + 273.15))] +
A2*Exp[ Ea2/(8.314*(44 + 273.15))] +
A3*Exp[Ea3/(8.314*(44 + 273.15))] == 0.00995,
A1*Exp[Ea1/(8.314*(41 + 273.15))] +
A2*Exp[ Ea2/(8.314*(41 + 273.15))] +
A3*Exp[Ea3/(8.314*(41 + 273.15))] == 0.0075,
Sqrt[A1*A1*Exp[2*Ea1/(8.314*(48 + 273.15))] +
A2*A2*Exp[2*Ea2/(8.314*(48 + 273.15))] +
A3*A3*Exp[2*Ea3/(8.314*(48 + 273.15))] +
2*A1*A2*Exp[(Ea1 + Ea2)/(8.314*(48 + 273.15))] +
2*A3*A2*Exp[(Ea3 + Ea2)/(8.314*(48 + 273.15))] -
2*A1*A3*Exp[(Ea1 + Ea3)/(8.314*(48 + 273.15))]] == 0.01784,
Sqrt[A1*A1*Exp[2*Ea1/(8.314*(44 + 273.15))] +
A2*A2*Exp[2*Ea2/(8.314*(44 + 273.15))] +
A3*A3*Exp[2*Ea3/(8.314*(44 + 273.15))] +
2*A1*A2*Exp[(Ea1 + Ea2)/(8.314*(44 + 273.15))] +
2*A3*A2*Exp[(Ea3 + Ea2)/(8.314*(44 + 273.15))] -
2*A1*A3*Exp[(Ea1 + Ea3)/(8.314*(44 + 273.15))]] == 0.00983,
Sqrt[A1*A1*Exp[2*Ea1/(8.314*(41 + 273.15))] +
A2*A2*Exp[2*Ea2/(8.314*(41 + 273.15))] +
A3*A3*Exp[2*Ea3/(8.314*(41 + 273.15))] +
2*A1*A2*Exp[(Ea1 + Ea2)/(8.314*(41 + 273.15))] +
2*A3*A2*Exp[(Ea3 + Ea2)/(8.314*(41 + 273.15))] -
2*A1*A3*Exp[(Ea1 + Ea3)/(8.314*(41 + 273.15))]] == 0.00742}, {A1,
42000}, {A2, 716000}, {A3,
2000000}, {Ea1, -20000}, {Ea2, -22000}, {Ea3, -71000},
MaxIterations -> Infinity, AccuracyGoal -> Infinity]
------------------------------------------------------------------------------------------------------------------------------------------------
Other times I get error message like this one:
FindRoot::lstol: "
"The line search decreased the step size to within tolerance specified
by AccuracyGoal and PrecisionGoal but was unable to find a sufficient
decrease in the merit function. You may need more than
"MachinePrecision" digits of working precision to meet these
tolerances."
Can it be solved in a better way in Sympy. And shouldn't the
Mathematica itself perturb the initial values to get the answer even
if it takes some time.
Thanks for any help,
Nandan
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