I know in matlab, index start from 1, not 0; How come I get an error on line k1 saying index exceeds matrix dimension even though for loop starts from 2?

 real x1;
 real x2;
 span=[0,4];
 h=.04;
 x10=0;
 x20=1;
x1(1)=x10;
x2(1)=x20;
step= 100;
f=@(x1,x2) -3*x2;
f1=@(x1,x2)(1/3)*x1;
for j=2:step
    x1(j,1)=x1(j-1)+h;

    k1(j-1,1)=h*f( x1(j-1), x2(j-1)); % index exceeds matrix dimension

    k2(j-1,1)=h*f( x1(j-1)+h/2, x2(j-1)+0.5*k1(j-1) );

    k3(j-1,1)=h*f( x1(j-1)+h/2, x2(j-1)+0.5*k2(j-1) );

    k4(j-1,1)=h*f( x1(j-1)+h, x2(j-1)+k3(j-1) );

    y1(j,1)=x2(j-1)+(1/6)*(k1(j-1)+2*k2(j-1)+2*k3(j-1)+k4(j-1));
end

Answer 1

[Birdman]

Because you did not do any preallocation for k1, k2, k3 and k4. Add this code before your loop and after the definition of step:

 k1=zeros(step-1,1)
 k2=zeros(step-1,1)
 k3=zeros(step-1,1)
 k4=zeros(step-1,1)
 y1=zeros(step,1)