Index exceeds dimensions error

I'm trying to code the predictor-corrector method, but I keep getting an "Index exceeds dimensions", and I don't see where the error is.

%function[t y]=abmpc4(f,a,b,y0,h)
f=@(t,y)((y/t)-(y/t)^2);
h=0.1;
a=1;
b=2;
y0=1;
n=(b-a)/h;
t(1)=a;
y(1)=y0;
w=[];
s=[];
s(1)=a;
w(1)=y0;

%RK4 method to get initial values
for i=1:3
    k1=h*f(t,y);
    k2=h*f(t+(h/2),y+(k1/2));
    k3=h*f(t+(h/2),y+(k2/2));
    k4=h*f(t+h,y+k3);
    y=y+(k1+(2*k2)+(2*k3)+k4)/6;
    t=t+h;
    w=[w,y];
    s=[s,t];
end

%truevals(1,1)=y0;

%Adams-Bashforth 4-Step
% i=4;
%  y=y+(55/24)*h*f(s(i,1),w(i,1))-(59/24)*h*f(s(i-1,1),w(i-1,1))+(37/24)*h*f(s(i-2,1),w(i-2,1))-(9/24)*h*f(s(i-3,1),w(i-3,1)); %predictor
%  %t=t+h;
%  w(i+1,1)=y;
%  s(i+1,1)=t;
for i=4:n
    %truevals=g;
    t=t+h;
    y=y+(h/24)*(55*f(t(i),y(i))-59*f(t(i-1),y(i-1))+37*f(t(i-2),y(i-2))-9*f(t(i-3),y(i-3))); %predictor
    y=y+(h/24)*(9*f(t(i+1,1),y(i+1,1))+19*f(t(i,1),y(i,1))-5*f(t(i-1,1),y(i-1,1))+f(t(i-2,1),y(i-2,1))); %corrector
    w=[w,y];
    s=[s,t];
end

[KSSV]

You are trying to access t as a vector, but it is a scalar. Check it.

Answer 1

[Star Strider]

The error:

Index exceeds matrix dimensions.

Error in Elipses (line ###)
    y=y+(h/24)*(55*f(t(i),y(i))-59*f(t(i-1),y(i-1))+37*f(t(i-2),y(i-2))-9*f(t(i-3),y(i-3)));
    %predictor

The problem is that here ‘t’ is a (1x1) double and ‘i’ is 4. That condition with throw the error you see.

This situation:

q = pi
r = q(4)

will throw the same error.

[cee878]

How can I fix this?

[Star Strider]

It is difficult for me to follow your code. The solution is for ‘t’ and ‘y’ to be vectors, since you are also referring to previous values as well as current values.

It will probably be best to preallocate those vectors prior to the loop. Consider in your initial assignments:

t = [a 0 0 0];
y = [y0 0 0 0];
s = [a 0 0 0];
w = [y0 0 0 0];

Those assignments will create your necessary vectors.

[cee878]

Okay. I fixed it like this:

%function[t y]=abmpc4(f,a,b,y0,h)
f=@(t,y)((y/t)-(y/t)^2);
h=0.1;
a=1;
b=2;
y0=1;
n=(b-a)/h;
t(1,1)=a;
y(1,1)=y0;
w=zeros(n+1,1);
s=zeros(n+1,1);
s(1,1)=a;
w(1,1)=y0;

%RK4 method to get initial values
for i=1:3
    k1=h*f(t,y);
    k2=h*f(t+(h/2),y+(k1/2));
    k3=h*f(t+(h/2),y+(k2/2));
    k4=h*f(t+h,y+k3);
    y=y+(k1+(2*k2)+(2*k3)+k4)/6;
    t=t+h;
    w(i+1,1)=y;
    s(i+1,1)=t;
end

%truevals(1,1)=y0;

for i=4:n
    %truevals=g;
    r(i,1)=f(s(i),w(i));
    y=y+(h/24)*(55*r(i,1)-59*r(i-1,1)+37*r(i-2,1)-9*r(i-3,1)); %predictor
    display(y);
    t=t+h;
    y=y+(h/24)*(9*f(s(i+1,1),w(i+1,1))+19*r(i,1)-5*r(i-1,1)+r(i-2,1)); %corrector
    w(i+1,1)=y;
    s(i+1,1)=t;
end

But I don't get an error, but when my code runs, I get NaN values. I don't get what's wrong though.

[Star Strider]

You need to update the vectors in your loops by subscripting them.

For example:

for i=4:n-1
    . . .
    y(n+1) = y(n) + ...
    . . .
end

Then reference them appropriately in your other equations that use them, similar to what I outlined here. You will have to experiment.