Industrial Mathematics - Alexiades
Lab 4
Roots and Equilibria
Find the equilibria of the single-size Ostwald ripening model we have been discussing,
i.e. find the two 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. Then find the other root.
[ Do NOT confuse the initial size x* with initial guess(es) for Newton Method ! ]
Find the roots ξ1 and ξ2 (at full double precision: 14 decimals)
1: when x* = 0.05 . Verify that ξ1 < ξ2 < x* ;
2: when x* = 0.0975 . Verify that ξ1 < x* < ξ2;
3: when x* = 0.08 and μ=1.e-5 . Verify that x* < ξ1 < ξ2.
In each case, discuss the physical meaning for the single-size
crystal model and what theory predicts.
Submit ONLY the following
in a text file "Lab4.txt":
Name, date, Lab4
======================================================= (separator line)
roots and discussion for Case 1
------------------------------------------------------- (separator line)
roots and discussion for Case 2
------------------------------------------------------- (separator line)
roots and discussion for Case 3
======================================================= (separator line)
your main program (that calls your Newton solver)
======================================================= (separator line)
your FCN subprogram (that evaluates F and DF)
NOTE:
The parameters pertain only to the function, so should be entered in the FCN subprogram.
You cannot use " * " in variable names in a code!
Can use "xstar", "cstar".