| Savitribai Phule Pune University |
| Title | Higher order numerical methods for fractional delay differential equation |
| Author/s |
Manoj Kumar
Department of Mathematics, National Defence Academy, Khadakwasala, Pune, 411023, India 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 | In this paper, we present a new family of higher-order numerical methods for solving non-linear fractional delay differential equations (FDDEs) along with the error analysis. Further, we solve various non-trivial systems of FDDEs to illustrate their applicability and utility. By using the proposed numerical methods, computational time is reduced drastically. These methods take only 5 to 10 percent of the time required for other methods such as the fractional Adams method (FAM). Furthermore, these methods converge for very small values of fractional derivative while FAM and the new predictor-corrector method (NPCM) introduced by Daftardar-Gejji et al. [1] do not converge. The order of convergence of the proposed methods is , where r is the order of fractional backward difference formulae and denotes the order of the fractional derivative. Thus these methods have a higher order of accuracy than FAM or NPCM. |
| Keywords | |
| Download | Journal |
| Citing This Document | Manoj Kumar, Aman Jhinga, and Varsha Daftardar-Gejji , Higher order numerical methods for fractional delay differential equation . Technical Report CMS-TR-20240405 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. | Published as Indian Journal of Pure and Applied Mathematics (Springer) 2024 |
| Contact | vsgejji AT gmail.com |
| Supplementary Material |