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Bridging Theory and Computation: The Double ZZ Transform for Nonlinear Integro-Partial Differential Equations
  • Mountassir Hamdi Cherif 1, *,   
  • Djelloul Ziane 2,   
  • Lakhdar Riabi 1,   
  • Waleed Adel 3

Received: 09 Jan 2026 | Revised: 25 Feb 2026 | Accepted: 14 Apr 2026 | Published: 01 Jun 2026

Abstract

This research investigates the theoretical foundations and computational implementation of the Double ZZ Transform (DZZT) for solving nonlinear integro-partial differential equations. By establishing the transform's existence theorem and core properties, this study provides a systematic approach to handling non-homogeneous models. The double ZZ transform method (DZZT), defined via two coupled integrals, emerges as a powerful analytical tool for tackling nonlinear partial differential equations prevalent in complex dynamical systems. The efficacy of this framework is demonstrated through the exact resolution of Fisher and Burger equations, supported by numerical simulations that confirm the method's accuracy.

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Hamdi Cherif, M.; Ziane, D.; Riabi, L.; Adel, W. Bridging Theory and Computation: The Double ZZ Transform for Nonlinear Integro-Partial Differential Equations . Nonlinear Analysis and Computer Simulations 2026, 1 (2), 10. https://doi.org/10.53941/nacs.2026.100010.
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