Finding root of nonlinear functions

Please, how do I find all the roots this function:

y-0.8193318913*tanh(y)+0.2931044702e-2*tanh(y)/(0.7500000000e-3*y^2-0.1622336517e-1) = 0

Answer 1

[Torsten]

f = @(y)(y-0.8193318913*tanh(y)).*(0.7500000000e-3*y.^2-0.1622336517e-1)+0.2931044702e-2*tanh(y);
fun = @(y)f(y)./(0.7500000000e-3*y.^2-0.1622336517e-1);
y = -6:0.01:6;
plot(y,f(y))

x0 = [-5 -4];
s(1) = fzero(f,x0);
x0 = [-1 1];
s(2) = fzero(f,x0);
x0 = [4 5];
s(3) = fzero(f,x0);
s

s = 1×3

-4.5365 0 4.5365

fun(s)

ans = 1×3

1.0e-14 * 0.4951 0 -0.4951

[Sam Chak]

👍, Yes, follow this method to find all real roots.

Answer 2

[Sam Chak]

Hi @University Glasgow

Read about fzero().

https://www.mathworks.com/help/optim/ug/fzero.html

The solution may look like this:

fun = @(y) y - 0.8193318913*tanh(y) + (0.2931044702e-2)*tanh(y)./(0.7500000000e-3*y.^2 - 0.1622336517e-1);
y0  = 0;        % initial guess
y   = fzero(fun, y0)

y = 0

[University Glasgow]

Thank you