Comparative Analysis of Iterative and Transform Methods for a (3+1)-Dimensional q-Deformed Dynamical Model

• Khalid K. Ali ^[1] ; Ahmed S. Shehata ^[2] ; Ahmet Bekir ^[3]
  1. [1] Sohar University, Al-Azhar University
  2. [2] Misr University for Science and Tech
  3. [3] Neighbourhood of Akcaglan

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• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 25, Nº 5, 2026
• Idioma: inglés
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• Resumen

  • This paper presents a systematic comparative analysis of two semi-analytical approaches, namely the Reduced q-Differential Transform Method (RqDTM) and the Variational Iteration Method (VIM), for solving a generalized (3+1)-dimensional q-deformed sinh-Gordon dynamical model. The principal novelty of this study lies in the application and systematic comparison of these methods to this high-dimensional q-deformed system, which has not been previously investigated in a unified comparative framework. Explicit recurrence relations and solution representations are derived for two physically relevant cases of the model. Numerical simulations are carried out to evaluate the accuracy and convergence behavior of both approaches under different parameter settings. The obtained results reveal excellent agreement between the analytical and numerical solutions, with absolute errors remaining on the order of 10−4 to 10−6 for the investigated parameter ranges, confirming the reliability and efficiency of the proposed methods. Comparisons with previously reported results further validate the correctness of the developed solutions. The study demonstrates that both RqDTM and VIM provide effective computational frameworks for solving high-dimensional q-deformed nonlinear equations, with VIM offering simpler implementation and RqDTM providing more systematic series construction. These methods offer valuable tools for the analysis of complex dynamical systems arising in mathematical physics and related interdisciplinary applications.

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