How to use Runge-Kutta orde 4 in sigmoid equation. I want to plot sigmoid equation with Runge kutta orde 4th but my graph is linear. I need help

This is my function

%This is my Runge Kutta for sigmoid equation
S=0;
    for j = 1:length(t)-1 
    k1S = dt*fRK4S(S(j));
    k2S = dt*fRK4S(S(j)+k1S/2);
    k3S = dt*fRK4S(S(j)+k2S/2);
    k4S = dt*fRK4S(S(j)+k3S);
    S(j+1) = S(j)+1/6*(k1S+2*k2S+2*k3S+k4S);
    end
    plot (S)
    

Answer 1

[VBBV]

You need to pass both t & S parameters to function fRK4S according to Runge-Kutte 4th order scheme

%This is my Runge Kutta for sigmoid equation
S(1)= 1; dt = 0.5;
a = 0; b = 10;
t = 0:dt:10; N = 100;
h = (b-a)/N;
for j = 1:length(t)-1 
    k1S = fRK4S(t(j),S(j));
    k2S = fRK4S(t(j)+h/2,S(j)+(h*k1S)/2);
    k3S = fRK4S(t(j)+h/2,S(j)+(h*k2S)/2);
    k4S = fRK4S(t(j)+h, S(j)+h*k3S);
    S(j+1) = S(j)+(1/6)*(k1S+2*k2S+2*k3S+k4S);  
end

plot(t,S); grid

function  S = fRK4S(t,S)
    S = S/(1+exp(-t));
end

[cindyawati cindyawati]

Thank you for your respon @VBBV but I already try, I get error

[Torsten]

You didn't copy VBBV's code correctly.

Look at what is written in your code when you look at the line

S(j+1) = S(j)+(1/6)*(k1S+2*k2S+2*k3S+k4S); 

[cindyawati cindyawati]

sorry,but i already correctly my picture and still can't run

[Torsten]

Did you change your function according to

function  dS = fRK4S(t,S)
  dS = S/(1+exp(-t));
end

?

What do you get as output if you insert the two lines

size(t)
size(S)

before the plot command ?

[cindyawati cindyawati]

Thank you @VBBV It is work!

Answer 2

[Torsten]

Why do you use a method for ordinary differential equations to integrate a simple function of the independent variable ?

Use "integral" instead or

syms T
f = 1/(1+exp(-T));
F = int(f,0,T);
F = matlabFunction(F);
T = 0:0.25:10;
plot(T,F(T))