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← 04-19 Infinity Time

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Showing Revision 2 created 10/24/2012 by Amara Bot.

  1. The Euler forward method is pretty simple again and the time
  2. that you should find for the explosion should be 0.64.
  3. This is a diagram resulting from that setting and this really makes it obvious that the solution
  4. is escaping to infinity and a finite amount of time.
  5. Actually, this behavior is not that much of a surprise.
  6. X always has to grow because the right hand side is always positive.
  7. The square is always positive and if you're adding to it and dividing by a positive number,
  8. but as x grows, the square is going to become really huge,
  9. so the rate of change becomes really huge, which leads to x become even higher and so and so on.
  10. This is going to escape to infinity in a finite amount of time.
  11. Footnote for the mathematically proficient, what we're getting here
  12. is actually the shifted version of the tangent function.