Dear all,
I want to know about the newest techniques about solving ODEs and PDEs by using uncertain methods like Interval Analysis, Affine Arithmetic, Improved of them, etc.
Did you know any better approaches or Ideas?
Numerical methods (algorithms) always work, and you can control your error by requiring it to be less than a certain value. This is as long as you have enough computational resources.
dear Vicente Mendoza Reyes,
Numerical methods (Like spectral methods, RKs, ...) are kinds of tools for the final solving these theories. I mean, I am looking for theories with more robustness than approaches like interval or Affine Arithmetics. Do you have any Idea?
I've heard that ANN (Artificial Neural Networks) are now being used as an approach to solving ODEs and PDEs. However, I do not know a lot about this area.
Thansks dear Vania Vieira Estrela,
I read about 4 books an very papers about this subject and the main reference is this one that you uploaded nicely. My major was (still is :D) on using soft computing methods for solving these kinds of systems. But now, after reading classical methods, I think they are still keep their priority in some cases.
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