Hi I'm new to matlab and I'm trying to run this code for Runge Kutta but I get an error at line 14.

function rk4_systems_trial()

alpha = [1 -1 2];
m = size(alpha,1);
if m == 1
   alpha = alpha';
end

h = 0.02;                                               %the step size
x(1) = 1;                                               %initial conditions
w(:,1) = alpha;                                         %col 1 of matrix w

for i = 1:4                                             %i=1,2,3,4
   k1 = h*f(x(i), w(:,i));
   k2 = h*f(x(i)+h/2, w(:,i)+0.5*k1);
   k3 = h*f(x(i)+h/2, w(:,i)+0.5*k2); 
   k4 = h*f(x(i)+h, w(:,i)+k3);
   w(:,i+1) = w(:,i) + (k1 + 2*k2 + 2*k3 + k4)/6;
   x(i+1) = 1 + i*h;
end

[x' w']

function dy = f(x, y)
dy = [y(2);
      y(3);
     y(1)*(x+1)^2 +y(2)*(x+1) + y(3)*6 + cos(ln(x+1))];

[CS Researcher]

What is the error? Have you defined w somewhere before this? If not, use w = alpha instead.

Answer 1

[Walter Roberson]

MATLAB uses log rather than ln

In your lines

dy = [y(2);
    y(3);
   y(1)*(x+1)^2 +y(2)*(x+1) + y(3)*6 + cos(ln(x+1))];

the space between the ^2 and the +y(2) is being interpreted as if you have two adjacent array elements, sort of like if you had written

dy = [1;
      2;
      3 4]

This would not happen if you used a space after the "+",

 dy = [y(2);
      y(3);
     y(1)*(x+1)^2 + y(2)*(x+1) + y(3)*6 + cos(log(x+1))];

Inside [], when there is a space followed by a "+" or a "-" that is not followed by a space, and the whole is not inside (), then the space is interpreted as indicating a new element, and the "+" or "-" are taken as "unary plus" or "unary minus". It is the difference between

[3 +4] or [3 -4]

and

[3 + 4] or [3 - 4] or [3+4] or [3-4]