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

Maan A. Rasheed; Raad Awad Hameed; Amal Nouman Khalaf

doi:10.24996/ijs.2023.64.1.33

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.