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← 02-08 Error Estimate

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

  1. So now we know that when we compare the result of the forward Euler method,
  2. it's going to deviate from the exact solution.
  3. Now assume that you have two numerical solutions.
  4. One solution with the forward Euler method of step size h1 and another with a step size of h2
  5. larger than h1, and assume that these two and the exact solution almost line up.
  6. The question then is--can we estimate the error between this numerical solution
  7. and the exact solution that we do not know based on the difference
  8. between those two numerical solutions, which we know.
  9. So given the distance between two solutions using the forward Euler method,
  10. how would you estimate the error between the exact solution
  11. and this first solution with the step size h1?
  12. Should it be E times the ratio, E times the ratio of the difference to the first step size,
  13. E times the ratio of the first step size to the difference, or E times the inverse ratio?