# Errors while trying to setup equation for root finding.

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Tom Goodland on 12 Jan 2022
Commented: Walter Roberson on 16 Jan 2022
I am trying to set up an equation for root finding to find a, however in the code at the bottom i get an error saying Parse error: Parse error at '=' . usage might be invalid syntax. Does anyone know how to fix this? I'd be grateful for any help.
x_pdo = z_pdo/(1 + a(k_pdo - 1));
x_water = z_water/(1 + a(k_water - 1));
x_glycerol = z_glycerol/(1 + a(k_glycerol - 1));
x_pdo + x_water + x_glycerol - 1 = 0;
Tom Goodland on 12 Jan 2022
my mistake yeah the x_... are unknown, do you know what function I should use to try to determine a (constant) and x_...? I'm pretty sure fzero would work but I get the error a is an unrecognised function or variable. Do you know any code that would be able to calculate a from the code i've posted as information, if you need anymore information let me know.
Thanks for the help

James Tursa on 12 Jan 2022
Did you mean multiply by the "a"?
x_pdo = z_pdo/(1 + a*(k_pdo - 1));
x_water = z_water/(1 + a*(k_water - 1));
x_glycerol = z_glycerol/(1 + a*(k_glycerol - 1));
Tom Goodland on 12 Jan 2022
yes do you have to put the * to multiply a by the bracket?

Torsten on 12 Jan 2022
Edited: Torsten on 12 Jan 2022
function main
a0 = 1;
a = fzero(@fun,a0)
end
function res = fun(a)
z_pdo = ...;
k_pdo = ...;
z_water = ...;
k_water = ...;
z_glycerol = ...;
k_glycerol = ...;
res = z_pdo/(1 + a*(k_pdo - 1)) + z_water/(1 + a*(k_water - 1)) + z_glycerol/(1 + a*(k_glycerol - 1)) -1.0;
end
Walter Roberson on 16 Jan 2022
if a is the same as α then α(kj-1) is 0 when α is 0, and 1+0 is 1, so xj = zj/stuff would be xj=zj/1...

Walter Roberson on 12 Jan 2022
syms a k_pdo x_pdo x_glycerol z_pdo z_glycerol k_glycerol k_water x_water z_water
eqn1 = x_pdo == z_pdo/(1 + a*(k_pdo - 1));
eqn2 = x_water == z_water/(1 + a*(k_water - 1));
eqn3 = x_glycerol == z_glycerol/(1 + a*(k_glycerol - 1));
eqn4 = x_pdo + x_water + x_glycerol - 1 == 0;
eqns = [eqn1; eqn2; eqn3; eqn4]
eqns = sol = solve(eqns, [a, x_pdo, x_glycerol x_water])
sol = struct with fields:
a: [3×1 sym] x_pdo: [3×1 sym] x_glycerol: [3×1 sym] x_water: [3×1 sym]
sols = [sol.a, sol.x_pdo, sol.x_glycerol, sol.x_water]
sols = sol3 = solve(eqns, [a, x_pdo, x_glycerol x_water], 'maxdegree', 3);
sol3s = [sol3.a, sol3.x_pdo, sol3.x_glycerol, sol3.x_water];
vpa(sol3s)
ans = R2021b

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