ON Numerical Blow-Up Solutions of Semilinear Heat Equations

  • 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
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.

Published
2020-08-28
How to Cite
Rasheed, M. A., Hameed, R. A., Obeid, S. K., & Jameel, A. F. (2020). ON Numerical Blow-Up Solutions of Semilinear Heat Equations. Iraqi Journal of Science, 61(8), 2077-2086. https://doi.org/10.24996/ijs.2020.61.8.23
Section
Mathematics