Numerical Blow-up Time of a One-Dimensional Semilinear Parabolic Equation with a Gradient Term

Authors

  • Maan A. Rasheed Department of Mathematics, College of Basic Education, Mustansiriyah University, Baghdad, Iraq https://orcid.org/0000-0002-7955-1424
  • Raad Awad Hameed Department of Mathematics, College of Education for Pure Science, Tikrit University, Tikrit, Iraq
  • Amal Nouman Khalaf Department of Mathematics, College of Education for Pure Science, Tikrit University, Tikrit, Iraq

DOI:

https://doi.org/10.24996/ijs.2023.64.1.33

Keywords:

Blow-up solutions, Blow-up time, Semilinear Heat Equation, Gradient term, Euler explicit (implicit) finite difference schemes

Abstract

  This paper deals with numerical approximations of a one-dimensional semilinear parabolic equation with a gradient term. Firstly, we derive the semidiscrete problem of the considered problem and discuss its convergence and blow-up properties. Secondly, we propose both Euler explicit and implicit finite differences methods with a non-fixed time-stepping procedure to estimate the numerical blow-up time of the considered problem. Finally, two numerical experiments are given to illustrate the efficiency, accuracy, and numerical order of convergence of the proposed schemes.

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Published

2023-01-30

Issue

Section

Mathematics

How to Cite

Numerical Blow-up Time of a One-Dimensional Semilinear Parabolic Equation with a Gradient Term. (2023). Iraqi Journal of Science, 64(1), 354-364. https://doi.org/10.24996/ijs.2023.64.1.33

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