How to solve for gamma

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smith
smith 2022-12-2
评论： smith 2022-12-5
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 个评论
Torsten
Torsten 2022-12-2
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
smith 2022-12-2
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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采纳的回答

Torsten
Torsten 2022-12-2
编辑：Torsten 2022-12-2
Ran in:
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 个评论
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Torsten
Torsten 2022-12-5
编辑：Torsten 2022-12-5
Ran in:
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

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