# How to solve for gamma

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smith am 2 Dez. 2022
Kommentiert: smith am 5 Dez. 2022
Hello, I'm trying to solve for gamma in this equation, I was hoping if someone can help out.
considering everything else is a constant that can be put as an input.
##### 2 KommentareKeine anzeigenKeine ausblenden
Torsten am 2 Dez. 2022
An analytical expression for gamma does not seem possible.
Use "fzero" or "fsolve" as numerical root finders for
left-hand side(gamma) - right-hand side(gamma) = 0
smith am 2 Dez. 2022
Hello, I tried but It's not solving.
clc
clear all
dbs=5.3e-10;
das=1.01e-9;
cb=4e3;
ca=1e3;
x0 =0;
x = fsolve(@myfun,x0)
function F = myfun(x)
F = (1-erf(sqrt(x/dbs)))-(((cb/ca)*sqrt(dbs/das))*(erf(sqrt(x/das)))*(exp((x/das)-(x/dbs))));
end

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### Akzeptierte Antwort

Torsten am 2 Dez. 2022
Bearbeitet: Torsten am 2 Dez. 2022
format long
dbs=5.3e-10;
das=1.01e-9;
cb=4e3;
ca=1e3;
x0 =0;
options = optimset('TolX',1e-14,'TolFun',1e-14);
x = fsolve(@(x)myfun(x,dbs,das,cb,ca),x0,options)
Equation solved. fsolve completed because the vector of function values is near zero as measured by the value of the function tolerance, and the problem appears regular as measured by the gradient.
x =
2.980227787591144e-08
myfun(x,dbs,das,cb,ca)
ans =
-7.180679523372318e-12
function F = myfun(x,dbs,das,cb,ca)
F = (1-erf(sqrt(x/dbs)))-(((cb/ca)*sqrt(dbs/das))*(erf(sqrt(x/das)))*(exp((x/das)-(x/dbs))));
end
##### 5 Kommentare3 ältere Kommentare anzeigen3 ältere Kommentare ausblenden
Torsten am 5 Dez. 2022
Bearbeitet: Torsten am 5 Dez. 2022
Seems your equation has multiple solutions.
A good idea is always to plot the function to have a good guess for the solution.
dbs=5.3e-10;
das=1.01e-9;
cb=4e3;
ca=1e3;
F = @(x)(1-erf(sqrt(x/dbs)))-(((cb/ca)*sqrt(dbs/das))*(erf(sqrt(x/das))).*(exp((x/das)-(x/dbs))));
x = 0:1e-12:2e-10;
plot(x,F(x))
sol = fzero(F,[0 1e-9])
sol = 4.7822e-11
F(sol)
ans = 1.2922e-09
smith am 5 Dez. 2022
Thank you @Torsten!

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