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

  • Koichi Anada
  • Tetsuya Ishiwata
  • Takeo UshijimaEmail author
Original Paper Area 1


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.


Blow-up rate Rescaling algorithm Numerical method 

Mathematics Subject Classification

65L99 65M99 



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.


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Copyright information

© The JJIAM Publishing Committee and Springer Japan KK 2017

Authors and Affiliations

  1. 1.Waseda University Senior High SchoolNerima-kuJapan
  2. 2.Department of Mathematical SciencesShibaura Institute of TechnologyMinuma-kuJapan
  3. 3.Deparment of Mathematics, Faculty of Science and TechnologyTokyo University of ScienceNodaJapan

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