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← Shrink The Error - Differential Equations in Action

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Showing Revision 3 created 05/24/2016 by Udacity Robot.

  1. You should be using 1.8 times the original number of steps.
  2. The original error before I change the number of steps would be something like this.
  3. Let's call it the old error would be a constant times the old step size to the fourth power.
  4. What I want to achieve is that the new error with the new step size is just the 10th part of this,
  5. and at the same time, because this is supposed to be a solver of order 4,
  6. this is the same constant as before times the new step size to the fourth power.
  7. So now we've got two equations that involved the old error and that constant C,
  8. this is the first one, this is the second one,
  9. we can solve for the new step size which is just basic algebra
  10. and you'll find that the new step size is the old step size divided by the ⁴√10
  11. and the ⁴√10 is about 1.8.
  12. So we are reducing the step size by a factor of 1.8
  13. which means that we are increasing the number of steps by that very factor of 1.8.