MATLAB: Runge Kutta 5th order help, error message “Index exceeds matrix dimensions.”

differential equationsrunge kutta

Hello I have written the following code for a second order differential equation, split into two first order differential equations using the 5th order Runge Kutta method but keep getting the error message "Index exceeds matrix dimensions.". Could someone please explain how to resolve this error? My original equations are:
dt/dx=z
dz/dx=(h*p/k*ac)*(t-ta)
Start of code:
ac=7.854*10^-7 %cross sectional area
k=110; % Conductive heat transfer coefficient
ta=25; % Room temperature
h=20; %Convective heat transfer coefficient
p=0.04063; %Perimeter of cylinder
s=0.001 %step size
xfinal=0.02; % final distance
N=xfinal/s; 
x(1)=0; %initial values
t(1)=50;
z(1)=0;
dtdx=@(x,t,z) z;
dzdx=@(x,t,z) (h*p/k*ac)*(t-ta);
for i=1:N
k1= dtdx(x(i),t(i),z(i));
l1=dzdx(x(i),t(i),z(i));
k2=dtdx(x(i)+0.25*s,t(i)+0.25*k1*s,z(i)+0.25*l1*s)
l2=dzdx(x(i)+0.25*s,t(i)+0.25*k1*s,z(i)+0.25*l1*s)
k3=dtdx(x(i)+0.25*s,t(i)+0.125*k1*s+0.125*k2*s,z(i)+0.125*l1*s+0.125*l2*s)
l3=dzdx(x(i)+0.25*s,t(i)+0.125*k1*s+0.125*k2*s,z(i)+0.125*l1*s+0.125*l2*s)
k4=dtdx(x(i)+0.5*s,t(i)-0.5*k2*s+k3*s,z(i)-0.5*l2*s+l3*s)
l4=dzdx(x(i)+0.5*s,t(i)-0.5*k2*s+k3*s,z(i)-0.5*l2*s+l3*s)
k5=dtdx(x(i)+0.75*s,t(i)+0.1875*k1*s+0.5625*k4*s,z(i)+0.1875*l1*s+0.5625*l4*s)
l5=dzdx(x(i)+0.75*s,t(i)+0.1875*k1*s+0.5625*k4*s,z(i)+0.1875*l1*s+0.5625*l4*s)
k6=dtdx(x(i)+s,t(i)-0.4286*k1*s+0.2857*k2*s+1.7143*k3*s-1.7143*k4*s+1.1429*k5*s,z(i)-0.4286*l1*s+0.2857*l2*s+1.7143*l3*s-1.7143*l4*s+1.1429*l5*s)
l6=dzdx(x(i)+s,t(i)-0.4286*k1*s+0.2857*k2*s+1.7143*k3*s-1.7143*k4*s+1.1429*k5*s,z(i)-0.4286*l1*s+0.2857*l2*s+1.7143*l3*s-1.7143*l4*s+1.1429*l5*s)
t(i+1)=t(i)*0.0111*(7*k1+32*k3+12*k4+32*k5+7*k6)*h
z(i+1)=z(i)*0.0111*(7*l1+32*l3+12*l4+32*l5+7*l6)*h
end

Best Answer

You don't have any x(i+1)=etc line. Since you don't set the next value of x, when you get to the second loop iteration the x(2) reference fails.
Related Question