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

• Published in: Japan journal of industrial and applied mathematics Vol. 35; no. 1; pp. 33 - 47
• Main Authors: Anada, Koichi, Ishiwata, Tetsuya, Ushijima, Takeo
• Format: Journal Article
• Language: English
• Published: Tokyo Springer Japan 01-03-2018; Springer Nature B.V
• Subjects: Applications of Mathematics; Chaos theory; Computational Mathematics and Numerical Analysis; Estimation; Evolutionary algorithms; Invariance; Mathematics; Mathematics and Statistics; Nonlinear equations; Nonlinear evolution equations; Nonlinear programming; Numerical analysis; Numerical methods; Original Paper; Rescaling; Scaling; Rescaling algorithm; Numerical method; 65M99; Blow-up rate; 65L99
• ISSN: 0916-7005; 1868-937X
• DOI: 10.1007/s13160-017-0273-9

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.