講題：On the numerical solutions for a parabolic system with blow-up
講者：卓建宏 教授 (國立中山大學應用數學系)
時間：110年12月6日(星期一)上午10：00-12：00
地點：民生校區五育樓4樓402教室
摘要
We study the finite difference approximation for axisymmetric solutions of a parabolic system with blow-up. A scheme with adaptive temporal increments is commonly used to compute an approximate blow-up time. There are, however, some limitations to reproduce the blow-up behaviors for such schemes. We thus use an algorithm, in which uniform temporal grids are used, for the computation of the blow-up time and blow-up behaviors. In addition to the convergence of the numerical blow-up time, we also study various blow-up behaviors numerically, including the blow- up set, blow-up rate and blow-up in Lσ-norm. To compute the blow-up behaviors, we need to compute the numerical blow-up times corresponding to each component respectively, though they converge to the same value, and analyze the numerical behaviors for each component at their numerical blow-up times. The relation between blow-up of the exact solution and that of the numerical solution is also analyzed and discussed.