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

Document Type : Research Paper

Authors

1 Department of Applied Mathematics, Bandar Anzali Branch, Islamic Azad University, Bandar Anzali , Iran

2 Department of Applied Mathematics and Computer Science, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran

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.

Keywords

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Volume 13, Issue 1
March 2022
Pages 783-789
  • Receive Date: 25 June 2021
  • Revise Date: 06 September 2021
  • Accept Date: 23 September 2021