Skip to main content
SpringerLink
Log in

On the computation of the numerical blow-up time

  • Original Paper
  • Area 1
  • Published:
Japan Journal of Industrial and Applied Mathematics Aims and scope Submit manuscript

Abstract

For certain evolution equations, we mean by the word “blow-up” that the solutions become unbounded in finite time T. The finite time T is called the blow-up time. In this paper, we propose an algorithm to compute the blow-up time by using a finite difference scheme with uniform temporal grid size.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Abia L., López-Marcos J.C., Martínez J.: The Euler method in the numerical integration of reaction-diffusion problems with blow-up. Appl. Numer. Math. 38, 287–313 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  2. Bandle H.: Blow-up in diffusion equations: a survey. J. Comp. Appl. Math. 97, 3–22 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  3. Chen Y.G.: Asymptotic behaviours of blowing-up solutions for finite difference analogue of u t =  u xx +  u 1+α. J. Fac. Sci. Univ. Tokyo 33, 541–574 (1986)

    MATH  Google Scholar 

  4. Cho C-.H.: On the convergence of numerical blow-up time for a second order nonlinear ordinary differential equation. Appl. Math. Lett. 24(3), 49–54 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  5. Cho C.H., Hamada S., Okamoto H.: On the finite differnece approximation for a parabolic blow-up problem. Japan J. Ind. Appl. Math. 24(2), 131–160 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  6. Friedman A., McLoed B.: Blow-up of positive solutions of semilinear heat equation. Indiana Univ. Math. J. 34, 425–447 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  7. Groisman P.: Totally discrete explicit and semi-implicit Euler methods for a blow-up problem in several space dimensions. Computing 76, 325–352 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  8. Levine H.A.: The role of critical exponents in blow up theorems. SIAM Rev. 32, 262–288 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  9. Nakagawa T.: Blowing up of a finite difference solution to u t =  u xx +  u 2. Appl. Math. Optim. 2, 337–350 (1976)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, National Chung Cheng University, Min-Hsiung, Chia-Yi, 621, Taiwan

    Chien-Hong Cho

Authors
  1. Chien-Hong Cho
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Chien-Hong Cho.

About this article

Cite this article

Cho, CH. On the computation of the numerical blow-up time. Japan J. Indust. Appl. Math. 30, 331–349 (2013). https://doi.org/10.1007/s13160-013-0101-9

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13160-013-0101-9

Keywords

Mathematics Subject Classification

Search

Navigation