the Runge-Kutta integration scheme

implement Runge-Kutta integration scheme with the delta=0.005

dx/dt=-x*(2-y), t0=0, x(t0)=1
dy/dt=y*(1-2*x), t0=0, y(t0)=2

but I am not sure the matlab code for Runge-Kutta integration method 4 steps

May anyone help me please?

Many thanks for helping!

[Jan]

Whoops? You have deleted the code of your Runge-Kutta implementation from the question. Why?

[Lam Chun Ting]

Because I think my matlab code is wrong, so that's why I delete it...and I am trying to do a new one as well ..

[Jan]

You can find a lot of Runge-Kutta implementations in the net. I suggest to use one of them and convert it to Matlab. If you get problems, post the code you have and ask for a specific line of code.

[Lam Chun Ting]

I try this in another way however, I think the phase curve is not right..Can you tell where did I get wrong please?

The following is my matlab code

function [x_out,y_out,t_out]=Runge_Kutta1(Delta_in,T0,T)
% setting up parameters of the integration
t_max=T;
t_min=T0;
Delta=Delta_in;
t=t_min:Delta:t_max;
 x=zeros(1,size(t,2));
y=zeros(1,size(t,2));
 z=zeros(1,2);
z(1)=1; 
z(2)=2; 
for i=1:size(t,2)
x(i)=z(1);
y(i)=z(2);
z1=competing_species_rhs2([z(1),z(2)]);
z2=competing_species_rhs2([z(1)+Delta/2,z(2)+Delta/2*z1]);
z3=competing_species_rhs2([z(1)+Delta/2,z(2)+Delta/2*z2]);
z4=competing_species_rhs2([z(1)+Delta,z(2)+Delta/2]);
z=z+Delta*((z1+2*z2+2*z3+z4)/6);
end;
t_out=t;
x_out=x;
y_out=y;

 function z_out=competing_species_rhs2(z)
  p=zeros(1,2);
  p(1)=-z(1)*(2-z(2));
  p(2)=z(2)*(1-2*z(1));
  z_out=p;

Many thanks for helping!!

Answer 1

[Jan]

You can compare the results of your function with the one calculated by Matlab's ODE45. Which differences do you see?