MATLAB: How to apply runge kutta method for system of equations that are coupled ODE’s? like x1’= -3*x2 and x2’=(1/3)*x1? I tried the code below but get an error on function define saying too may input arguments.

MATLAB

 y=zeros(1,length(x));
 z=zeros(1,length(x));
 y(1)=0;
 z(1)=0;
 Fx1= @(x2)(3)*x2;
 Gx2=@(x1)(1/3)*x1;
 for i=2:(length(x)-1)
    k1=Fx1(x(i),y(i));
    g1=Gx2(x(i),y(i));
    k2=Fx1(x(i)+0.5*h,y(i)+0.5*h*k1);
    g2=Gx2(x(i)+0.5*h,y(i)+0.5*h*g1);
    k3=Fx1((x(i)+0.5*h),(y(i)+0.5*h*k2));
    g3=Gx2((x(i)+0.5*h),(y(i)+0.5*h*g2));
    k4=Fx1((x(i)+h),(y(i)+k3*h));
    g4=Gx2((x(i)+h),(y(i)+g3*h));
   y(i+1)=y(i)+(1/6)*(k1+2*k2+2*k3+k4)*h;
    z(i+1)=y(i)+(1/6)*(g1+2*g2+2*g3+g4)*h;

Best Answer

In all of your for loop, even though your Fx1 and Gx2 functions are defined for one input argument, you try to pass two input arguments. You need to either change your code in for loop, or change your function definitions before for loop.
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