Mathematica NDSolve conditions help

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Discussion Overview

The discussion revolves around troubleshooting an issue with the NDSolve function in Mathematica, specifically related to the interpretation of initial conditions in a system of differential equations. Participants explore potential causes and solutions for the error encountered when setting these conditions.

Discussion Character

  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant describes an error message indicating that NDSolve is interpreting initial conditions as "False" rather than valid equations.
  • The same participant shares their code and the context in which the error occurs, suggesting that the initial conditions might be incorrectly formatted.
  • Another participant notes that they do not encounter the same error using a different version of Mathematica, suggesting a possible version-related issue.
  • A later reply mentions that restarting Mathematica resolved the issue, raising questions about the state of the kernel and its impact on the execution of the code.
  • One participant speculates that previous assignments to the derivatives x'[0] and y'[0] might have interfered with the current definitions, leading to the error.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the underlying cause of the problem, with multiple hypotheses presented regarding the error's origin and resolution.

Contextual Notes

The discussion highlights potential limitations related to the state of the Mathematica kernel and how it may affect the interpretation of variable assignments and initial conditions.

Hertz
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Hi, I'm having a problem with NDSolve in mathematica where it is interpreting my initial conditions as "True" or "False".

Here is the code:
Code:
soln = NDSolve[{eqn1[[1]], eqn1[[2]], x[0] == y[0] == 0, x'[0] == 1, 
    y'[0] == 0}, {x, y}, t];

where eqn1 is determined by the following code:
Code:
Clear[soln, eqn1, xeqn, yeqn, eqn, sink, source, field,  k, m, a,  f, F, U]
a = 1;
sink = {0, 
    a} - (1/(x^2 + (y - a)^2))*(x^2 + (y - a)^2)^(-1/2)*{x, y - a};
source = {0, -a} + (1/(x^2 + (y + a)^2))*(x^2 + (y + a)^2)^(-1/2)*{x, 
     y + a};
field = sink + source;
F = m*k*field;
U[x_, y_] = Integrate[F[[1]], x] + Integrate[F[[2]], y];
T = (m/2) (x'[t]^2 + y'[t]^2);
L = T - U[x[t], y[t]];
xeqn = D[L, x[t]] == D[D[L, x'[t]], t];
yeqn = D[L, y[t]] == D[D[L, y'[t]], t];
eqn = {xeqn, yeqn};
eqn1 = eqn /. {k -> 1, m -> 1}

Here is the error:
Code:
NDSolve::deqn: Equation or list of equations expected instead of False in the first argument
{eqn1[[1]], eqn1[[2]], x[0] == y[0] == 0, False, False}

It looks to me like I must be typing my velocity initial conditions in wrong or something, but every example I can find online does it this same way. I've also tried typing it in other ways like using the D function etc, but I keep having the same issue. :\
 
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Interesting. I don't get an error using Mathematica 9.0. Try quitting your kernel and re-running it.
 
Wow, I was almost certain that wasn't going to work. I've been dealing with the problem for a long time now, just never bothered to ask. Turns out, restarting mathematica fixed it though. I just did a restart and copy/pasted what was here.

Is there anything to take from this? Any ideas why that might have happened? I wonder if saving my work and restarting mathematica would have also worked. Guess I'll have to experiment more later on.
 
It looks like somehow y'[0] and x'[0] were previously set to some specific value, and it was causing problems.
 

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