ON Numerical Blow-Up Solutions of Semilinear Heat Equations

Authors

  • Maan A. Rasheed Department of Mathematics, College of Basic Education, Mustansiriyah University, Baghdad, Iraq
  • Raad A. Hameed Department of Mathematics, College of Education, Tikrit University, Tikrit, Iraq
  • Sameer K. Obeid Department of Mathematics, College of Education, Tikrit University, Tikrit, Iraq
  • Ali F. Jameel School of Quantitative Sciences, College of Arts and Sciences, Universitiy Utara Malaysia (UUM), Sintok, Kedah, Malaysia

DOI:

https://doi.org/10.24996/ijs.2020.61.8.23

Keywords:

Blow-up solution, Semi-linear Heat equation, Dirichlet boundary conditions, Explicit Euler Scheme, Implicit Euler Scheme

Abstract

This paper is concerned with the numerical blow-up solutions of semi-linear heat equations, where the nonlinear terms are of power type functions, with zero Dirichlet boundary conditions. We use explicit linear and implicit Euler finite difference schemes with a special time-steps formula to compute the blow-up solutions, and to estimate the blow-up times for three numerical experiments. Moreover, we calculate the error bounds and the numerical order of convergence arise from using these methods. Finally, we carry out the numerical simulations to the discrete graphs obtained from using these methods to support the numerical results and to confirm some known blow-up properties for the studied problems.

Downloads

Download data is not yet available.

Downloads

Published

2020-08-28

Issue

Section

Mathematics

How to Cite

ON Numerical Blow-Up Solutions of Semilinear Heat Equations. (2020). Iraqi Journal of Science, 61(8), 2077-2086. https://doi.org/10.24996/ijs.2020.61.8.23

Similar Articles

1-10 of 1131

You may also start an advanced similarity search for this article.

Most read articles by the same author(s)