ncku-talk2018-04-12

Colloquium

DATE 2018-04-12　16:10-17:00

PLACE 數學館3174教室

SPEAKER 卓建宏副教授（中正大學數學系）

TITLE A Numerical Algorithm for Blow-up Problem

ABSTRACT In many evolution equations, solutions may become unbounded in finite time. This phenomenon is often called blow-up and the finite time is called the blow-up time. To numerically reproduce the finite-time blow-up phenomenon, schemes with adaptive time meshes were considered to be necessary. Since the numerical blow-up time is defined by an infinite sum, which implies that one needs to compute infinite times to achieve blow-up, this method cannot be carried out in real computation. As a consequence, we propose an algorithm accomplished by schemes with uniform time meshes for the computation of blow-up solutions. In this talk, we are concerned with a question: to what extent can this algorithm be applied to compute the blow-up solutions and reproduce the blow-up behavior?

Colloquium

DATE	2018-04-12　16:10-17:00

PLACE	數學館3174教室

SPEAKER	卓建宏副教授（中正大學數學系）

TITLE	A Numerical Algorithm for Blow-up Problem

ABSTRACT	In many evolution equations, solutions may become unbounded in finite time. This phenomenon is often called blow-up and the finite time is called the blow-up time. To numerically reproduce the finite-time blow-up phenomenon, schemes with adaptive time meshes were considered to be necessary. Since the numerical blow-up time is defined by an infinite sum, which implies that one needs to compute infinite times to achieve blow-up, this method cannot be carried out in real computation. As a consequence, we propose an algorithm accomplished by schemes with uniform time meshes for the computation of blow-up solutions. In this talk, we are concerned with a question: to what extent can this algorithm be applied to compute the blow-up solutions and reproduce the blow-up behavior?