| Savitribai Phule Pune University |
| Title | Computational Approaches to Time-Fractional Partial Differential Equation |
| Author/s |
Aman Jhinga
Department of Mathematics and Computer Science, West University of Timişoara, 300223, Timişoara, Romania Varsha Daftardar-Gejji Department of Scientific Computing, Modeling and Simulation, Savitribai Phule Pune University, Pune 411 007, India |
| Abstract | This study introduces innovative numerical methods that exhibit superior computational efficiency in solving three distinct types of equations, each involving fractional derivatives in time. These equations include the time-fractional advection-dispersion equation, the time-fractional wave-diffusion equation, and the multi-term time-fractional wave-diffusion 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. |
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| Citing This Document | Aman Jhinga, and Varsha Daftardar-Gejji , Computational Approaches to Time-Fractional Partial Differential Equation . Technical Report CMS-TR-20240327 of the Centre for Modeling and Simulation, Savitribai Phule Pune University, Pune 411007, India (2024); available at http://scms.unipune.ac.in/reports/. |
| Notes, Published Reference, Etc. | Under review. |
| Contact | vsgejji AT gmail.com |
| Supplementary Material |