ncku-talk2010-11-11

NCTS(South)/ NCKU Math Colloquium

DATE 2010-11-11　16:10-17:00

PLACE R204, 2F, NCTS, NCKU

SPEAKER 卓建宏Chien-Hong Cho　（國立中正大學）

TITLE On the finite difference approximation for hyperbolic blow-up problems

ABSTRACT We consider the CLM equation as a example showing the difficulties in reproducing blow-up numerically. Then we consider the semilinear wave equation $u_{tt}=u_{xx}+u^2$ and its finite difference analogue whose time mesh is adaptively-defined. We show not only that our numerical solution blows up in finite time but also that the numerical blow-up time converges to the real blow-up time under certain assumptions.
However, it is difficult to show the stability of the numerical solution if the time mesh varies every step. Our recent results will be reported

NCTS(South)/ NCKU Math Colloquium

DATE	2010-11-11　16:10-17:00

PLACE	R204, 2F, NCTS, NCKU

SPEAKER	卓建宏Chien-Hong Cho　（國立中正大學）

TITLE	On the finite difference approximation for hyperbolic blow-up problems

ABSTRACT	We consider the CLM equation as a example showing the difficulties in reproducing blow-up numerically. Then we consider the semilinear wave equation $u_{tt}=u_{xx}+u^2$ and its finite difference analogue whose time mesh is adaptively-defined. We show not only that our numerical solution blows up in finite time but also that the numerical blow-up time converges to the real blow-up time under certain assumptions. However, it is difficult to show the stability of the numerical solution if the time mesh varies every step. Our recent results will be reported