channelflow.org

A bare-bones Newton search code for solving the nonlinear equation //f(x) = 0//. <code> function x = newtonsearch(f,x) % return x that solves f(x) == 0, using input argument x as initial guess eps = 1e-14; % tolerance 1e-14 == 1 x 10^(-14) dx = 1e-07; % increment for approximating slope df/dx fx = f(x); while (abs(fx) > eps) % approximate slope f'(x) fx_dx = f(x+dx); fprime = (fx_dx - fx)/dx; % solve for newton step delta_x delta_x = -fx/fprime; % set new guess for x to x + delta_x and compute new f(x) x = x + delta_x; fx = f(x); end </code>