Nonlinear PDE Days

** **

**Kaori
Nagatou **

**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.`