Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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ESTIMATING THE BLOW-UP TIME FOR CHIPOT-WEISSLER EQUATION USING CRANK-NICOLSON METHOD

  • MAAN A. RASHEED (Department of Mathematics, College of Basic Education, Mustansiriyah University) ;
  • RAAD AWAD HAMEED (Department of Mathematics, College of Education for Pure Science, Tikrit University) ;
  • AMAL NOUMAN KHALAF (Computer Systems Department, Kirkuk Technical Institute, Northern Technical University) ;
  • HIBA ALI KAREEM (College of Science for Women, University of Baghdad)
  • Received : 2024.06.05
  • Accepted : 2024.12.04
  • Published : 2025.01.30
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Abstract

This paper is devoted to study the numerical blow-up solutions of Chipot-Weissler equation, which is a one-dimensional semilinear parabolic equation with a gradient term. In the first part, we derive the semidiscrete problem of the considered problem and discuss its convergence and blow-up properties. Then, we propose Crank-Nicolson finite differences methods with a non-fixed time-stepping procedure to estimate the numerical blow-up time of the considered problem. Moreover, we investigate the consistency, stability and convergence of the proposed scheme. In the last part, two numerical experiments are given to illustrate the efficiency, accuracy, and numerical order of convergence of the proposed method.

Keywords

Acknowledgement

The authors would like to thank the reviewers for their positive comments and remarks that helped in improving this work.

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