Nonlinear Equations

Octave can solve sets of nonlinear equations of the form

F (x) = 0

using the function fsolve, which is based on the MINPACK subroutine hybrd.

Loadable Function: [x, info] = fsolve (fcn, x0)

Given fcn, the name of a function of the form f (x) and an initial starting point x0, fsolve solves the set of equations such that f(x) == 0.

Loadable Function: fsolve_options (opt, val)

When called with two arguments, this function allows you set options parameters for the function fsolve. Given one argument, fsolve_options returns the value of the corresponding option. If no arguments are supplied, the names of all the available options and their current values are displayed.

Here is a complete example. To solve the set of equations

-2x^2 + 3xy   + 4 sin(y) = 6
 3x^2 - 2xy^2 + 3 cos(x) = -4

you first need to write a function to compute the value of the given function. For example:

function y = f (x)
  y(1) = -2*x(1)^2 + 3*x(1)*x(2)   + 4*sin(x(2)) - 6;
  y(2) =  3*x(1)^2 - 2*x(1)*x(2)^2 + 3*cos(x(1)) + 4;
endfunction

Then, call fsolve with a specified initial condition to find the roots of the system of equations. For example, given the function f defined above,

[x, info] = fsolve ("f", [1; 2])

results in the solution

x =

  0.57983
  2.54621

info = 1

A value of info = 1 indicates that the solution has converged.

The function perror may be used to print English messages corresponding to the numeric error codes. For example,

perror ("fsolve", 1)
     -| solution converged to requested tolerance

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