A Pseudo-Spectral Approach to Solving the Fractional Cable Equation Using Lagrange Polynomials

Document Type : Research Article

Authors

Department of Mathematics, Faculty of Sciences, University of Zanjan, Zanjan, Iran

Abstract

This paper focuses on addressing the fractional cable equation through the pseudo-spectral method, providing an innovative approach for solving problems in fractional calculus. The proposed method utilizes Lagrange polynomials at Chebyshev points to approximate spatial derivatives, ensuring high computational precision. One of the noteworthy features of this study is the time discretization scheme introduced, which is unconditionally stable and boasts a convergence order of $\mathcal{O}(\tau^2)$. Such stability is crucial for solving time-dependent fractional differential equations, especially when long-term simulations are required. Pseudo-spectral methods are known for their exponential accuracy, and the approach detailed in this paper exemplifies this capability. To demonstrate the robustness and reliability of the proposed technique, several numerical examples are presented. These examples highlight the method's efficiency in achieving highly accurate solutions with minimal computational effort. By leveraging spectral techniques, this research offers insights into solving fractional differential equations with greater precision, paving the way for future advancements in this field. The outcomes underscore the proposed method's effectiveness and emphasize its potential applicability to a broad range of scientific and engineering problems.

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Analytical and Numerical Solutions for Nonlinear Equations
Volume 9, Issue 1
May 2024
Pages 20-33

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History

  • Receive Date: 23 January 2025
  • Revise Date: 16 April 2025
  • Accept Date: 23 April 2025
  • Publish Date: 20 April 2025

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