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<p>This study introduces innovative numerical methods that exhibit superior computational efficiency in solving three distinct types of equations, each involving fractional derivatives in time which include the time-fractional advection-dispersion equation, the time-fractional diffusion-wave equation, and the multi-term time-fractional diffusion-wave equation. The stability and convergence analysis of these methods is performed and their effectiveness is further substantiated through a series of numerical examples. A comparative analysis is also conducted between the numerical errors of the new methods and those of existing methods documented in the literature. The results of this comparison reveal that the newly introduced methods have better accuracy. Thus this approach is a significant development in the realm of numerical analysis of fractional partial differential equations.</p>

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Computational approaches to time-fractional partial differential equations

  • 期刊论文

  • 发表日期：

    2026年4月29日

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  • Aman Jhinga,
  • Varsha Daftardar-Gejji

摘要

This study introduces innovative numerical methods that exhibit superior computational efficiency in solving three distinct types of equations, each involving fractional derivatives in time which include the time-fractional advection-dispersion equation, the time-fractional diffusion-wave equation, and the multi-term time-fractional diffusion-wave equation. The stability and convergence analysis of these methods is performed and their effectiveness is further substantiated through a series of numerical examples. A comparative analysis is also conducted between the numerical errors of the new methods and those of existing methods documented in the literature. The results of this comparison reveal that the newly introduced methods have better accuracy. Thus this approach is a significant development in the realm of numerical analysis of fractional partial differential equations.