Numerical Blow-up Time of a One-Dimensional Semilinear Parabolic Equation with a Gradient Term
Blow-up solutions
Blow-up time
Semilinear Heat Equation
Gradient term
Euler explicit (implicit) finite difference schemes
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.
