| Author | Message | |||
     Martin van der Schans (martin) Junior Member Username: martin Post Number: 3 Registered: 12-2005 |
The problem I'm try to model is the heat equation from the disk D^2 to the sphere S^2. See the attatchment If we set epsilon=0 it is the heat equation from D^2 to S^2. For small epsilon one can prove that the solution looks similar in regions bounded away from 0. In the epsilon=0 case the solution makes a jump from 0 to 1 and eventually jumps back. The model works fine except for the fact that if epsilon is getting too small it seems that it doesn't make any difference any moore. But it should make difference since for epsilon too small one would need more and more mesh points to control the error. How can it be that flexpde does not seem to run in too trouble for very small epsilon (say 10^50 or something like that)?
| |||
| Martin van der Schans (martin) Member Username: martin Post Number: 4 Registered: 12-2005 |
sorry in the last line I meant 10^-50 | |||
| Robert G. Nelson (rgnelson) Moderator Username: rgnelson Post Number: 610 Registered: 06-2003 |
Computers do not store numbers in infinite precision. The standard double-precision storage format contains 52 bits in the fraction part and 12 bits in the exponent part. This corresponds to about 16 decimal digits. If you compute 1+eps, then for eps smaller than 1e-16, the result is exactly 1. eps less than 1e-16 relative to other terms in the arithemtic operation is effectively zero. |
Harmonic map heat flow