[
    {
        "id": "osp-13614",
        "type": "article-journal",
        "title": "Analysis of Fractional Linear Multi-Step Methods of Order Four from Super-Convergence",
        "author": [
            {
                "family": "Nasir",
                "given": "Haniffa Mohamed"
            },
            {
                "family": "Al Hasani",
                "given": "Khadija"
            }
        ],
        "URL": "https://omanscience.com/en/articles/analysis-of-fractional-linear-multi-step-methods-of-order-four-from-super-convergence",
        "language": "en",
        "issued": {
            "date-parts": [
                [
                    2023
                ]
            ]
        },
        "container-title": "Sultan Qaboos University Journal for Science",
        "volume": "28",
        "issue": "2",
        "page": "44-55",
        "DOI": "10.53539/squjs.vol28iss2pp44-55",
        "publisher": "Sultan Qaboos University",
        "ISSN": "2308-3921",
        "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."
    }
]