Abstract
We present and investigate a new type of implicit fractional linear multi-step method of order two for fractional initial value problems. The method is obtained from the second-order superconvergence of the Grünwald-Letnikov approximation of the fractional derivative at a non-integer shift point. The method coincides with the backward difference method of order two for the classical initial value problem when the order of the derivative is one. The weight coefficients of the proposed method are obtained from the Grünwald weights and are hence computationally efficient compared with that of the fractional backward difference formula of order two. The stability properties are analyzed and it is shown that the stability region of the method is larger than that of the fractional Adams-Moulton method of order two and the fractional trapezoidal method. Numerical results and illustrations are presented to justify the analytical theories.
Keywords
Publication details
- DOI
- 10.53539/squjs.vol27iss2pp107-118
- Journal
- Sultan Qaboos University Journal for Science, 27(2), 107-118
- Publisher
- Sultan Qaboos University
- Open access
- Gold open access
- License
- CC BY-ND 4.0
Cite this article
APA 7
Nasir, H. M. (2023). Analysis of New Type of Second-order Fractional Linear Multi-step Method with Improved Stability. Sultan Qaboos University Journal for Science, 27(2), 107-118. https://doi.org/10.53539/squjs.vol27iss2pp107-118
MLA 9
Nasir, Haniffa Mohamed. "Analysis of New Type of Second-order Fractional Linear Multi-step Method with Improved Stability." Sultan Qaboos University Journal for Science, vol. 27, no. 2, 2023, pp. 107-118. https://doi.org/10.53539/squjs.vol27iss2pp107-118.
Chicago (author–date)
Nasir, Haniffa Mohamed. 2023. "Analysis of New Type of Second-order Fractional Linear Multi-step Method with Improved Stability." Sultan Qaboos University Journal for Science 27 (2): 107-118. https://doi.org/10.53539/squjs.vol27iss2pp107-118.
Harvard
Nasir, H. M. (2023) 'Analysis of New Type of Second-order Fractional Linear Multi-step Method with Improved Stability', Sultan Qaboos University Journal for Science, 27(2), pp. 107-118. doi:10.53539/squjs.vol27iss2pp107-118.
Vancouver
Nasir HM. Analysis of New Type of Second-order Fractional Linear Multi-step Method with Improved Stability. Sultan Qaboos University Journal for Science. 2023;27(2):107-118. doi:10.53539/squjs.vol27iss2pp107-118
IEEE
H. M. Nasir, "Analysis of New Type of Second-order Fractional Linear Multi-step Method with Improved Stability," Sultan Qaboos University Journal for Science, vol. 27, no. 2, pp. 107-118, 2023, doi: 10.53539/squjs.vol27iss2pp107-118.