4th order Runge-Kutta Method Help

Below is my code for a 4th order Runge-Kutta but I keep getting an error and I don't see what I am doing wrong. I was hoping somebody could help point me in the right direction to fix my code.

Answer 1

[James Tursa]

You never set the z2 elements inside your loop, so on the second iteration when z2(i-1) is used (with i=3) z2(2) does not exist. I am guessing you need to add a line like this after setting z1(i):

    z2(i) = z2(i-1)+((1/6)*(k1z2+2*k2z2+2*k3z2+k4z2));

Also, it appears you have a typo in your z1(i) assignment. That last * should be a + instead. E.g.,

    z1(i) = z1(i-1)+((1/6)*(k1z1+2*k2z1+2*k3z1*k4z1));

should be

    z1(i) = z1(i-1)+((1/6)*(k1z1+2*k2z1+2*k3z1+k4z1));

Finally, as a readability advice I would suggest you put some spaces in your code. E.g., I think this is much more readable (and easier to spot bugs):

    z1(i) = z1(i-1) + (1/6) * (k1z1 + 2*k2z1 + 2*k3z1 + k4z1);
    z2(i) = z2(i-1) + (1/6) * (k1z2 + 2*k2z2 + 2*k3z2 + k4z2);

[WhatIsMatlab-]

Thank you!! That did the trick. I took your advice on adding the spacing. You are 100% right it makes it a lot easier to see what is happening in my code. Thank you again.

Answer 2

[Torsten]

   dz2dx = @(z1,z2) 2*z2 5*z1;

There is no connector between z2 and 5 in the expression above.

Best wishes

Torsten.

[WhatIsMatlab-]

Sorry there should be a plus sign there. But that doesn't fix the problem. That was an error from copying the code over.