الملخص
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.
الكلمات المفتاحية
بيانات النشر
- المعرّف الرقمي
- 10.53539/squjs.vol28iss2pp44-55
- المجلة
- مجلة جامعة السلطان قابوس للعلوم, 28(2), 44-55
- الناشر
- جامعة السلطان قابوس
- وصول مفتوح
- وصول مفتوح ذهبي
- الترخيص
- CC BY-ND 4.0
اقتبس هذه المقالة
APA 7
Nasir, H. M., & Al Hasani, K. (2023). Analysis of Fractional Linear Multi-Step Methods of Order Four from Super-Convergence. Sultan Qaboos University Journal for Science, 28(2), 44-55. https://doi.org/10.53539/squjs.vol28iss2pp44-55
MLA 9
Nasir, Haniffa Mohamed, and Khadija Al Hasani. "Analysis of Fractional Linear Multi-Step Methods of Order Four from Super-Convergence." Sultan Qaboos University Journal for Science, vol. 28, no. 2, 2023, pp. 44-55. https://doi.org/10.53539/squjs.vol28iss2pp44-55.
شيكاغو (المؤلف–التاريخ)
Nasir, Haniffa Mohamed, and Khadija Al Hasani. 2023. "Analysis of Fractional Linear Multi-Step Methods of Order Four from Super-Convergence." Sultan Qaboos University Journal for Science 28 (2): 44-55. https://doi.org/10.53539/squjs.vol28iss2pp44-55.
هارفارد
Nasir, H. M. and Al Hasani, K. (2023) 'Analysis of Fractional Linear Multi-Step Methods of Order Four from Super-Convergence', Sultan Qaboos University Journal for Science, 28(2), pp. 44-55. doi:10.53539/squjs.vol28iss2pp44-55.
فانكوفر
Nasir HM, Al Hasani K. Analysis of Fractional Linear Multi-Step Methods of Order Four from Super-Convergence. Sultan Qaboos University Journal for Science. 2023;28(2):44-55. doi:10.53539/squjs.vol28iss2pp44-55
IEEE
H. M. Nasir, and K. Al Hasani, "Analysis of Fractional Linear Multi-Step Methods of Order Four from Super-Convergence," Sultan Qaboos University Journal for Science, vol. 28, no. 2, pp. 44-55, 2023, doi: 10.53539/squjs.vol28iss2pp44-55.