ODE SYSTEM OF EQUATION

Hi,

I'm trying to solve a system of ode's using Runge-kutta, i made a function for RK2(f,h,x0,y0,xfinal) and tried to solve the system shown below with specified IC's. Could someone help fix the code as I get errors and code doesnt work.

clear all
clc
beta=1/3;
gamma=1/7;

syms R S I
N=S+I+R;

ode1=-(beta*I*S)/N
ode2=-(beta*I*S)/N-gamma*I
ode3=gamma*I

odes=[ode1,ode2,ode3]


for j=odes
    RK2(j,0.2,0,8e6,7)
end
    


 
 function [xs,ys]=RK2(f,h,x0,y0,xfinal)
 f=matlabFunction(f);
 fprintf('\n x        y ');
 o=1;
while x0<=xn
    fprintf('\n%4.3f  %4.3f ',x0,y0); %values of x and y
    xs(o)=x0;
    ys(o)=y0;
    k1=h*f(x0,y0); 
    x1=x0+h; 
    k2=h*f(x1,y0+k1);
    y1=y0+(k1+k2)/2;           
    x0=x1;
    y0=y1;  
    o=o+1;
end


end
 

[darova]

I'd suggest you to try to solve use euler method first

Something like this:

% constants beta I N
ds = @(s) -beta*I*s/N;
dt = 0.1;
s = 0.1;
for i = 2:100    
    s(i+1) = s(i) + dt*ds(s(i));
end
plot(s)

Answer 1

[Guru Mohanty]

I understand you are trying to solve system of ODEs using RK iteration. The error occurred in the iteration due to following reasons-

1. Inside your ‘RK2’ function there is no defined value of ‘xn’.
2. Inside ‘RK2’ matlabFunction function converts Symbolic expression to function handle. So, the first ODE becomes 3 Variable function.
3. In the following code

    k1=h*f(x0,y0);

The code will error out because the function handle takes 3 inputs and, in the statement, only two inputs are present.

After Resolving these issues, the code should work.

[Faraz Vossoughian]

Hey thanks for your response, do you have a suggestion on how to fix the problem