Array indices must be positive integers or logical values.

Writing function for Runge Kutta 4th order. ERROR --> Array indices must be positive integers or logical values.

command window call is

dydx = @(x,y) (1+4*x)*sqrt(y)
 RungeKutta(dydx, 0, 1,0.25,1)

code below

function RungeKutta(f, L, U,h,y0)
%f = function 
% L = lower bound
% U = upper bound

% y0 = inital condition y value
%h = step size 
t = L:h:U;
n = length(t);
 % need for loop 
 k1 = zeros (1,n);
 k2 = zeros (1,n);
 k3 = zeros (1,n);
 k4 = zeros (1,n);
 y = zeros(1, n);
 for i = 0: n
        k1(i) = f(t(i),y(i));
        k2(i)  = f(t(i)+0.5*h,y(i)+0.5*k1(i)*h);
        k3(i) = f(t(i) + 0.5*h, y(i)+0.5*k2(i)*h);  
        k4(i) = f(t(i) + h, y(i) + k3(i)*h); 
        y(i+1) =  y(i) + (1/6)*(k1(i)+2*k2(i) + 2*k3(i)+k4(i))*h;
 
 end %end of fo loop 
 hold on
 title('Runge-Kutta Method')
 xlabel('X axis')
 ylabel('Y axis')
 plot(t, f(t),'b', x, y, 'r')
 legend('Original Plot', 'True Plot')
end % end of function

Answer 1

[James Tursa]

At least two problems. First, you need to start your for loop indexing at 1 instead of 0:

for i = 1: n-1 % ending at n-1 so that y stays at n elements

Second, you don't set the initial state of y before entering the loop. You need something like this prior to the loop:

y(1) = y0;

[Alexa Shumaker]

If change the for loop to i =1 it add another element in my y array so when I graph x is to 5 while y is to 6 elements and it doesnt work

[James Tursa]

Did you also see that I changed the upper bound to n-1?

[Alexa Shumaker]

Thank you!