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