@Article{, title={ON Numerical Blow-Up Solutions of Semilinear Heat Equations}, author={Maan A. Rasheed1 and Raad A. Hameed2 and Sameer K. Obeid3 and Ali F. Jameel3*}, journal={Iraqi Journal of Science المجلة العراقية للعلوم}, volume={61}, number={8}, pages={2077-2086}, year={2020}, 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.

} }