How do I discovery solution for nonlinear system?

I´m a new user of MaLab and this channel. I know that MatLab is a program with a big libery of functions to resolev problems. I want know where can I discovery way to solve nonlinear systems? I know have types forms like Newton-Raphson, Minimum square but I don´t know call this functions in MatLab.

Tks

Answer 1

[Walter Roberson]

fsolve(), vpasolve(), solve(), fzero() (and with extensions here)

[Ricardo Barbieri]

Tks for your help But Can you say to me what command use, what name method ? And the oders methods.

Tks

[Walter Roberson]

fsolve, from the Optimization toolbox, gives options for:

• trust-region-dogleg
• trust-region-reflective
• levenberg-marquardt

vpasolve() and solve() work with symbolic expressions. The methods they use to solve for non-linear equations depend upon whether the equations are polynomial or not. For non-polynomials, they use a Newton-type approach, according to http://www.mathworks.com/help/symbolic/mupad_ref/numeric-fsolve.html

The basic fzero, which is for a single function in a single variable, "uses a combination of bisection, secant, and inverse quadratic interpolation methods." I am not sure at the moment if there is a difference between that at the fzero of the optization toolbox

There are other approaches available which are not called "solving" but are called "optimizing", but which can often be adapted for "solving". For example if you have a non-linear equation then instead of "solving" it, you might instead ask to minimize the square of it. That would be "optimizing" for a value as close to 0 as possible, and provided there is a root in the region should give you a location very close to the root. Nonlinear systems are often difficult to find precise solutions to due to numeric difficulties. nonlinear least squares is one of the optimization routines available.

If you are looking specifically for routines to do Newton-Raphson, then Mathworks itself does not provide any. You can, however, find a number of user-contributed versions in the File Exchange -- I got tired after tagging 50 of them.