A higher order numerical scheme for solving fractional Bagley-Torvik equation

MATHEMATICAL METHODS IN THE APPLIED SCIENCES(2022)

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摘要
In this paper, we develop a higher order numerical method for the fractional Bagley-Torvik equation. The main tools used include a new fourth-order approximation for the fractional derivative based on the weighted shifted Grunwald-Letnikov difference operator and a discrete cubic spline approach. We show that the theoretical convergence order improves those of previous work. Five examples are further presented to illustrate the efficiency of our method and to compare with other methods in the literature.
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关键词
discrete spline, fractional Bagley-Torvik equation, numerical solution, Weighted shifted Grunwald-Letnikov approximation
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