Scientific Computing, Modeling & Simulation
Savitribai Phule Pune University

Technical Report CMS-TR-20240405


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 Timi┼čoara, 300223, Timi┼čoara, 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


ProgrammesOpenCourseWare | Research & ConsultancyReports
About | PeopleAlumni | Announcements | Apps | Contact



© Scientific Computing, Modeling & Simulation • Savitribai Phule Pune University