Bridging Theory and Computation: The Double ZZ Transform for Nonlinear Integro-Partial Differential Equations

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.