Document Type : Research Paper
Department of Applied Mathematics, Bandar Anzali Branch, Islamic Azad University, Bandar Anzali , Iran
Department of Applied Mathematics and Computer Science, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran
This article deals with the nonlinear parabolic equation with piecewise continuous arguments (EPCA). This study, therefore, with the aid of the $\theta$ -methods, aims at presenting a numerical solution scheme for solving such types of equations which has applications in certain ecological studies. Moreover, the convergence and stability of our proposed numerical method are investigated.
Finally, to support and confirm our theoretical results, some numerical examples are also presented.