A numerical scheme for solving nonlinear parabolic partial differential equations with piecewise constant arguments

Abstract

‎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.