Equation exceeding matrix dimensions

I get a ??? Index exceeds matrix dimensions. error for the last line in the code. I am trying to define an equation u(i+1) that includes u(i) and u(i-1) (which is itself in a previous iteration) but ran into this problem.

i = 2:4000; p0 = 10; t1 = 5; dt = 0.05;

t = dt*i;

p(1) = p0*dt/t1;

p(i) = ...
 (p0*t/t1) .* (0 <= t & t < t1 ) + ...
 (p0) .* (t1 <= t & t < 2*t1  ) + ...
 (-p0*t/t1+3*p0) .* (2.*t1 <= t & t <= 3*t1) + ...
 (0) * (t > 3*t1);

u0 = 0; ud0 = 0; udd0 = 10;

un1 = u0 - dt*ud0 + (dt^2)*udd0/2;

u(1) = (p0 - un1 - u0);

u(2) = (p(1) - u0 - u(1));

u(i+1) = (p(i) - u(i-1) - u(i));

plot(t,u(i+1))

Answer 1

[Walter Roberson]

Your problem is with

u(i+1) = (p(i) - u(i-1) - u(i));

MATLAB processes all of the entries simultaneously, so it is going to be trying to access u(3:4000) at a time when only u(1) and u(2) have been defined. MATLAB does not handle such situations iteratively. If you want a difference equation based upon previous values, write it as a loop (or find a way to code it in terms of filter())