Mathematica Stack Exchange is a question and answer site for users of Mathematica. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I was wondering how to approximate or tabulate values for this numeric approximation: It is the following: The confusing part is how to implement the subscripts in mathematica.

$y_{i+1} = (t_i - y_i)h + y_i$

I want to do something of the following for this numeric solution.

x[t_] = t/(1 + t^4);
data = N[Table[{t, x[t]}, {t, -5, 5}], 2];
tableofcontents = Prepend[data, {"t", "x(t)"}];
Text@Grid[tableofcontents, Alignment -> Right, Dividers -> {Center, {False, True}}, 
  Spacings -> 1]

Mathematica graphics

share|improve this question
Look at RecurrenceTable[]. What are you actually trying to do, and what results are you expecting? – J. M. Apr 27 '12 at 17:32
what is the definition of $h$ and $t_i$? – Sjoerd C. de Vries Apr 27 '12 at 21:05
@SjoerdC.deVries: $h=1/n$, is the step size. $t_i$, is the time steps. – night owl Apr 29 '12 at 11:29
@J.M.: Approximate a solution to the equation in order to compare with the tabulated true solution values for the same time steps. – night owl Apr 29 '12 at 11:31
up vote 6 down vote accepted

I recommend you look at RecurrenceTable as J. M. suggested. However to give you an idea of how you would implement subscripts (by which I think you mean recursion) in a "normal" way, here's a simple example using the Fibonacci sequence:

f[0] = 1;
f[1] = 1;
f[n_] := f[n - 1] + f[n - 2];

For performance you would also "memoize", which just means that you store every result so that you don't have to recalculate it later:

f[0] = 1;
f[1] = 1;
f[n_] := (
   f[n] = f[n - 1] + f[n - 2]

Notice that the f[n] = within the function is not f[n_] :=, because we aren't matching to a generic pattern and we don't need to recalculate the expression every time it's used. We're telling Mathematica that f applied to the specific value that n has at that time is whatever it calculates on the right-hand side at that time, so the usage there is like array indexing. It's the same as was done in the first two lines specifying f[0] and f[1].

And for the sake of completeness, here's the RecurrenceTable version of the Fibonacci sequence that I pulled straight out of the documentation:

RecurrenceTable[{a[n] == a[n - 1] + a[n - 2], a[1] == 1, a[2] == 1}, a, {n, 10}]
share|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.