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<p>The current research investigation introduces a novel spectral method for solving two-dimensional time-fractional telegraph equations (2D-TFTE). The approach utilizes a tailored basis of generalized shifted Jacobi polynomials (GSJPs) constructed to automatically satisfy the given initial-boundary conditions (IBCs), leading to an efficient numerical framework. A cornerstone of the proposed methodology is the incorporation of operational matrices within the spectral framework, which elevates the precision and computational performance of the resulting numerical scheme. We also provide theoretical assurances of the method’s effectiveness via error and convergence analysis. Three test examples validate the suggested approach’s superior accuracy and effectiveness, benchmarking its performance against established techniques.</p>

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Efficient solutions for multidimensional time-fractional telegraph equations via spectral methods with generalized Jacobi Galerkin operational matrices

  • 期刊论文

  • 发表日期：

    2026年4月22日

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  • Hany Mostafa Ahmed,
  • Ramy M. Hafez,
  • Mohammad Izadi,
  • Yogeshwari F. Patel

摘要

The current research investigation introduces a novel spectral method for solving two-dimensional time-fractional telegraph equations (2D-TFTE). The approach utilizes a tailored basis of generalized shifted Jacobi polynomials (GSJPs) constructed to automatically satisfy the given initial-boundary conditions (IBCs), leading to an efficient numerical framework. A cornerstone of the proposed methodology is the incorporation of operational matrices within the spectral framework, which elevates the precision and computational performance of the resulting numerical scheme. We also provide theoretical assurances of the method’s effectiveness via error and convergence analysis. Three test examples validate the suggested approach’s superior accuracy and effectiveness, benchmarking its performance against established techniques.