A numerical method of estimating blow-up rates for nonlinear evolution equations by using rescaling algorithm

Koichi Anada; Tetsuya Ishiwata; Takeo Ushijima

doi:10.1007/s13160-017-0273-9

A numerical method of estimating blow-up rates for nonlinear evolution equations by using rescaling algorithm

Koichi Anada, Tetsuya Ishiwata, Takeo Ushijima^*

^*Corresponding author for this work

Waseda University Senior High School

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

In this paper, we proposed a numerical method for estimating blow-up rate of blow-up solutions for a class of nonlinear evolution equations which have a scaling invariance. To use this scaling invariance we adopt the rescaling algorithm to the problems and numerically estimate the blow-up rates. Applying the method to several examples, we examine the effectiveness of the method.

Original language	English
Pages (from-to)	33-47
Number of pages	15
Journal	Japan Journal of Industrial and Applied Mathematics
Volume	35
Issue number	1
DOIs	https://doi.org/10.1007/s13160-017-0273-9
Publication status	Published - 2018 Mar 1

Keywords

Blow-up rate
Numerical method
Rescaling algorithm

ASJC Scopus subject areas

Engineering(all)
Applied Mathematics

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10.1007/s13160-017-0273-9

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abstract = "In this paper, we proposed a numerical method for estimating blow-up rate of blow-up solutions for a class of nonlinear evolution equations which have a scaling invariance. To use this scaling invariance we adopt the rescaling algorithm to the problems and numerically estimate the blow-up rates. Applying the method to several examples, we examine the effectiveness of the method.",

keywords = "Blow-up rate, Numerical method, Rescaling algorithm",

author = "Koichi Anada and Tetsuya Ishiwata and Takeo Ushijima",

note = "Funding Information: Acknowledgements The second author is partially supported by JSPS KAKENHI Grant Numbers 15K13461 and 15H03632. The authors thank the referees for careful reading and invaluable comments on our manuscript. Publisher Copyright: {\textcopyright} 2017, The JJIAM Publishing Committee and Springer Japan KK.",

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AU - Anada, Koichi

AU - Ishiwata, Tetsuya

AU - Ushijima, Takeo

N1 - Funding Information: Acknowledgements The second author is partially supported by JSPS KAKENHI Grant Numbers 15K13461 and 15H03632. The authors thank the referees for careful reading and invaluable comments on our manuscript. Publisher Copyright: © 2017, The JJIAM Publishing Committee and Springer Japan KK.

PY - 2018/3/1

Y1 - 2018/3/1

N2 - In this paper, we proposed a numerical method for estimating blow-up rate of blow-up solutions for a class of nonlinear evolution equations which have a scaling invariance. To use this scaling invariance we adopt the rescaling algorithm to the problems and numerically estimate the blow-up rates. Applying the method to several examples, we examine the effectiveness of the method.

AB - In this paper, we proposed a numerical method for estimating blow-up rate of blow-up solutions for a class of nonlinear evolution equations which have a scaling invariance. To use this scaling invariance we adopt the rescaling algorithm to the problems and numerically estimate the blow-up rates. Applying the method to several examples, we examine the effectiveness of the method.

KW - Blow-up rate

KW - Numerical method

KW - Rescaling algorithm

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ER -

A numerical method of estimating blow-up rates for nonlinear evolution equations by using rescaling algorithm

Abstract

Keywords

ASJC Scopus subject areas

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