Convergence for the numerical blow up time of a nonlinear ODE problem

碩士 === 國立中正大學 === 數學系應用數學研究所 === 106 === We consider the frst order nonlinear ODE blow-up problem u′(t)=G(u). Nakagawa [6] proposed a scheme with adaptively-defned temporal increment for the computation of the blow-up solutions. Later, an algorithm using uniform time mesh was proposed by Cho [3] for...

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Bibliographic Details
Main Authors: DU, BI-YI, 杜碧怡
Other Authors: Cho, Chien-Hong
Format: Others
Language:en_US
Published: 2018
Online Access:http://ndltd.ncl.edu.tw/handle/php9kh
Description
Summary:碩士 === 國立中正大學 === 數學系應用數學研究所 === 106 === We consider the frst order nonlinear ODE blow-up problem u′(t)=G(u). Nakagawa [6] proposed a scheme with adaptively-defned temporal increment for the computation of the blow-up solutions. Later, an algorithm using uniform time mesh was proposed by Cho [3] for the computation of the numerical blow-up time. Nevertheless, these schemes are of order 1 in time variable so that the convergence order of the numerical blow-up time is also of order 1. In this presentation, we would like to consider a question as to can we have a higher convergence order if we use a higher order scheme for both methods to compute the blow-up time.