Numerical Blow-up Time of a One-Dimensional Semilinear Parabolic Equation with a Gradient Term
DOI:
https://doi.org/10.24996/ijs.2023.64.1.33Keywords:
Blow-up solutions, Blow-up time, Semilinear Heat Equation, Gradient term, Euler explicit (implicit) finite difference schemesAbstract
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.