Industrial Mathematics - Alexiades
Roots and Equilibria
Find the equilibria of the single-size Ostwald ripening model we have been discussing,
i.e. find the roots of the equation
μ x3 + c* exp( Γ/x ) = c1 , where c1 := c0 + μ (x*)3,
with parameter values:
μ=1.e-3, c*=7.52e-7, Γ=4.e-3, c0= 1.05 c*.
For a specified x* (see below), your code should solve the equation for x
(by calling your Newton solver), and print it out.
[ Do NOT confuse the initial size x* with initial guess(es) for Newton Method ! ]
Find the roots x1 and x2 (at full double precision: 15 decimals)
1: when x* = 0.05 . Verify that x1 < x2 < x* ;
2: when x* = 0.0975 . Verify that x1 < x* < x2;
3: when x* = 0.08 and μ=1.e-5 . Verify that x* < x1 < x2.
Discuss the physical meaning of these results for the single-size
crystal model and what theory predicts for each case.
Submit ONLY the following:
roots and discussion
your main program (that calls your Newton solver)
your FCN subprogram
The parameters pertain only to the function, so should be entered in the FCN subprogram.
You cannot use " * " in variable names in a code!
Could use "xstar", "cstar", or some other reasonable names...