Equations

Is it possible to solve an integral equation in matlab? I am writing a script for calculating some parameters in lake dynamics and one of the equation is the Schmidt stability:

S=(g/As).*int_{0}^{Zd}((Z-Zv).*rho.*Az)dz

where dz refers to partial z so integrate with respect to z.

If I have all of the variables which fit into the equation how do I go about solving it in matlab.

thanks

Answer 1

[Andrei Bobrov]

variant 1

S = ...;
g = ...;
As = ...;
Zv = ...;
rho = ...;
Az = ...;
out = fzero(@(Zd)S-g/As.*quad(@(Z)(Z-Zv).*rho.*Az,0,Zd),0);

please read doc fzero and doc quad

variant 2

syms S g As Z Zv rho Az Zd real
out1 = solve(S-g/As*int((Z-Zv)*rho*Az,Z,0,Zd),Zd)