ncku-talk2009-09-28

NCKU Math colloquium

DATE 2009-09-28　15:30-17:00

PLACE R204, 2F, NCTS, NCKU

SPEAKER Prof. Yuusuke Iso（Graduate School of Informatics, Kyoto University）

TITLE Finite Difference Methods for the Cauchy Problems in the Class of Analytic Functions

ABSTRACT Stability and Convergence are the most important mathematical concepts in numerical analysis for partial differential equations, and stability implies convergence of the consistent finite difference schemes for well-posed linear cases. In the talk, we will show that these two concepts are independent of each other in the class of analytic functions, and we show some numerical examples to illustrate it.
We will give a brief introduction of the theory of finite difference methods (FDM) applied to the Cauchy problems for linear partial differential equations, and we explain three basic concepts of consistency, convergence and stability. We apply FDM to some ill-posed Cauchy problems, which often arise in the analysis of inverse problems, and we show both a theory and computation about convergent schemes for ill-posed problems. The numerical examples are constructed by using multiple-precision arithmetic, whichh enables us to deal with hundreds and more digits in computation.
This is a joint work with Prof. Hiroshi Fujiwara, and his multiple-precision code 'exflib' is also introduced in the talk.

NCKU Math colloquium

DATE	2009-09-28　15:30-17:00

PLACE	R204, 2F, NCTS, NCKU

SPEAKER	Prof. Yuusuke Iso（Graduate School of Informatics, Kyoto University）

TITLE	Finite Difference Methods for the Cauchy Problems in the Class of Analytic Functions

ABSTRACT	Stability and Convergence are the most important mathematical concepts in numerical analysis for partial differential equations, and stability implies convergence of the consistent finite difference schemes for well-posed linear cases. In the talk, we will show that these two concepts are independent of each other in the class of analytic functions, and we show some numerical examples to illustrate it. We will give a brief introduction of the theory of finite difference methods (FDM) applied to the Cauchy problems for linear partial differential equations, and we explain three basic concepts of consistency, convergence and stability. We apply FDM to some ill-posed Cauchy problems, which often arise in the analysis of inverse problems, and we show both a theory and computation about convergent schemes for ill-posed problems. The numerical examples are constructed by using multiple-precision arithmetic, whichh enables us to deal with hundreds and more digits in computation. This is a joint work with Prof. Hiroshi Fujiwara, and his multiple-precision code 'exflib' is also introduced in the talk.