I need to set up a Runge Kutta solver for water leaving a bucket through a certain diameter nozzle as function of time, it says array indices must be positive integers/log val

rnoz=1.049/2

rtank=120/2

Dnoz=1.049

Dtank=120

g=386.088

t=10

h=60

y=(0:200)

N:50

y(1)=240

F_y =-(((rnoz^2)/(rtank^2))*sqrt((2*g)/(1-(Dnoz/Dtank)^4)))*sqrt(y(1))*h+y(1)

for i=0:60:200

k_1 = F_y(y(i))

k_2 = F_y(y(i)+0.5*h*k_1)

k_3 = F_y(y(i)+0.5*h*k_2)

k_4 = F_y(y(i)+k_3*h)

y(i+1) = y(i) + (1/6)*(k_1+2*k_2+2*k_3+k_4)*h

end

Answer 1

[Alan Stevens]

Indices in Matlab start at 1, not 0, so you need

for i=1:60:200

not

for i=0:60:200

[Christiaan Janeke]

So in responce to Alan Stevens answer I fixed that part, but once I tried to run the code agian, for my k_2 value it gave the error of: index exceeds the number of array elements.

[Christiaan Janeke]

Correction for k_1

[Alan Stevens]

You probably want to define your function F_y as

F_y = @(y) -(((rnoz^2)/(rtank^2))*sqrt((2*g)/(1-(Dnoz/Dtank)^4)))*sqrt(y)*h+y;

Also note that if you increment i by 60 each iteration, then your k values still won't make sense (they will be calculated incorrectly). Just let

i = 1: ceil(200/h); 

or something like that. (I suspect h = 60 is far too large a step size!).