0
$\begingroup$

" I have an assignment where I am required to use bisection or false position method depending on various inputs and I think I have a reasonable code that should work but I am not sure why I keep getting the errors at the bottom?"

----------


Func[f_, a_, b_, MaxIter_, eps_, flag_] := (
    atable = {a};
    btable = {b};
    xtable = {1};
    ErrorTable = {1};
    i = 1;
    Title = {"Iteration", "a", "b", "x_i", "f[a]", "f[b]", "f[x_i]", "er"};
    T2 = Table[{i, atable[ [i]], btable[ [i]], xtable[ [i]], f[atable[ [i]]],
    f[btable[ [i]]], f[xtable[ [i]]], ErrorTable[ [i]]}, {i, Length[xtable]}];
    If[Or[flag < 1, flag > 2], "Please select appropriate values (1 or 2) for flag",
    If[a > b, "Please select a < b",
    If[f[a] * f[b] > 0, "Please select appropriate values a and b such that f[a]*f[b]<0",
    While[And[i ≤ MaxIter, flag ⩵ 1],
    ri = (atable[ [i]] + btable[ [i]]) / 2;
    If[f[ri] * f[atable[ [i]]] ≤ 0, atable = Append[atable, atable[ [i]]];
    btable = Append[btable, ri],
    If[f[ri] f[btable[ [i]]] ≤ 0, btable = Append[btable, ri];
    btable = Append[btable, btable[ [i]]]]];
    If[i ⩵ 1, xtable[ [i]] = ri, xtable = Append[xtable, ri];
    ei = N[ (xtable[ [i]] - xtable[ [i - 1]]) / xtable[ [i]]];
    ErrorTable = Abs[Append[ErrorTable, ei]]];
    If[Abs[ErrorTable[ [i]] < eps], flag ⩵ 0, flag ⩵ 1];
    i ++];
    While[And[i ≤ MaxIter, flag ⩵ 2],
    ri = (atable * f[btable] - btable * f[atable]) / (f[btable] - f[atable]);
    If[f[ri] * f[atable[ [i]]] ≤ 0, atable = Append[atable, atable[ [i]]];
    btable = Append[btable, ri],
    If[f[ri] f[btable[ [i]]] ≤ 0, btable = Append[btable, ri];
    btable = Append[btable, btable[ [i]]];
    If[i ⩵ 1, xtable[ [i]] = ri, xtable = Append[xtable, ri];
    ei = N[ (xtable[ [i]] - xtable[ [i - 1]]) / xtable[ [i]]];
    ErrorTable = Abs[Append[ErrorTable, ei]];
    If[Abs[ErrorTable[ [i]] < eps], flag ⩵ 0, flag ⩵ 2];
    i ++]]]]];
    T2 = Prepend[T2, Title];
    T2 // MatrixForm]])

    f[x_] := x^3;
    Func[f, -3, 7, 100, 0.001, 1]


----------


  <  Part: Part 3 of {-3, -3} does not exist.
    Part: Part 3 of {-3, -3} does not exist.
    Part: Part 3 of {-3., -3.} does not exist.
    General: Further output of Part::partw will be suppressed during this calculation.>
Improve this question
$\endgroup$
5
  • $\begingroup$ I didn't take the time to actually understand your code, but you can try print statement debugging to get a better understanding of what's going on. For example, if you insert Print[i]; Print[{atable,btable,xtable}] right after While[And[i ≤ MaxIter, flag == 1], it becomes clear that on the third iteration, atable's length is only two and the program requests its third element, thus raising the error. Also, I've noticed a typo: in If[Abs[ErrorTable[[i]] < eps], flag == 0, flag == 1] there must be = instead of ==. $\endgroup$ – aooiiii Feb 2 '20 at 9:26
  • 1
    $\begingroup$ Your code seems much too dense and complicated. Can't you strip out the actual mechanics of the method from the rest, encapsulate that as a function, and debug that first; you might even write a separate function just to do one iteration of the method. Also, see, e.g., mathematica.stackexchange.com/questions/69771/…. $\endgroup$ – murray Feb 2 '20 at 16:45
  • $\begingroup$ When I ran your code I got no errors: i.stack.imgur.com/pKWIe.png -- I'm using V12, but at a glance I don't see any version-specific issues. $\endgroup$ – Michael E2 Feb 3 '20 at 2:39
  • 1
    $\begingroup$ @Michael E2 there were no errors and no meaningful output because for some weird reason all ==s in @miraj's code turned into a single unicode character ⩵ that Mathematica doesn't recognize. If you replace them back, the errors return. Should have written that in the first comment, but ran out of allowed space. $\endgroup$ – aooiiii Feb 3 '20 at 5:23
  • $\begingroup$ @aooiiii Yes but I think the OP should post code that reproduces the problem. Via an edit. $\endgroup$ – Michael E2 Feb 3 '20 at 14:18
0
$\begingroup$

More a comment, not a direct answer to your question of why those errors in your own code. You might start with the following, then add the code to supply tolerance specifications.

rfStep[f_, a_, b_] := (a f[b] - b f[a])/(f[b] - f[a])

regulaFalsiSimple[f_, a0_, b0_, n_] :=
 Module[
  {a = N[0], b = N[b0], c = rfStep[f, a0, b0], k},
  k = 0;
  While[k < n,
   If[Sign[f[b]] == Sign[f[c]],
    b = c, a = c];
   c = rfStep[f, a, b];
   k = k + 1];
  c]

f[x_] := x^3

regulaFalsiSimple[f, -3, 7, 100]
Improve this answer
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

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