Abstract
We analyze two implicit fractional linear multi-step methods of order four for solving fractional initial value problems. The methods are derived from the Grunwald-Letnikov approximation of fractional derivative at a non-integer shift point with super-convergence. The weight coefficients of the methods are computed from fundamental G unwald weights, making them computationally efficient when compared with other known methods of order four. We also show that the stability regions are larger than that of the fractional Adams-Moulton and fractional backward difference formula methods. We present numerical results and illustrations to verify that the theoretical results obtained are indeed satisfied.
Recommended Citation
Nasir, Haniffa Mohamed and Al Hasani, Khadija
(2025)
Analysis of Fractional Linear Multi-Step Methods of Order Four from Super-Convergence,
Sultan Qaboos University Journal For Science: Vol. 28:
Iss.
2, 44-55.
DOI: https://doi.org/10.53539/squjs.vol28iss2pp44-55
Available at:
https://squjs.squ.edu.om/squjs/vol28/iss2/2