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A novel operational collocation method for variable-order time-fractional diffusion-wave equations

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  • Sadri, Khadijeh
  • Amilo, David
  • Hinçal, Evren

Abstract

Time-fractional diffusion-wave equations (TFDWEs) effectively model various phenomena, including heat transfer, chemical and disease diffusion, reactive substance propagation, seismic wave dynamics, and signal transmission in electrical systems. This study presents an enhanced operational collocation method to solve TFDWEs with variable order. The proposed approach integrates the collocation technique with eighth-kind Chebyshev polynomials (EKCPs) as basis functions. To improve computational accuracy, new operational matrices for integer-order integrals in time and space are constructed using an innovative matrix framework. Additionally, a pseudo-operational matrix is developed to approximate variable-order integrals of the basis vector. The novel operational matrices comprise two components: an enhanced operational matrix and a supplementary vector. An error bound for the residual function is derived in a Chebyshev-weighted space. Comparative analysis with a second-order Chebyshev wavelets method demonstrates the efficacy of the proposed scheme, yielding small absolute errors.

Suggested Citation

  • Sadri, Khadijeh & Amilo, David & Hinçal, Evren, 2026. "A novel operational collocation method for variable-order time-fractional diffusion-wave equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 250(C), pages 592-614.
    • Handle: RePEc:eee:matcom:v:250:y:2026:i:c:p:592-614
    DOI: 10.1016/j.matcom.2026.07.012
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