Nonlinear PDE Days           Karlsruhe               January  20 – 21,  2011





Kaori Nagatou

Kyushu University, Fukuoka, Japan



Computer assisted proofs for nonlinear partial differential equations


Numerical methods which assure the reliability of the numerical results obtained by a computer, which
sometimes are also called "Numerical Verification Methods", have attracted a great deal of attention
in recent years. These methods assure not only a bound for the error between an approximate
solution and an exact solution, but also prove the existence of an exact solution within the computed
error bounds. This is why such methods are also called "Computer-Assisted Proofs". In particular,
cases can be covered where purely analytical methods have failed. In this talk, the basic concepts of
Computer Assisted Proofs for partial differential equations (in particular elliptic boundary value
problems) are presented together with some examples.





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