Abstract
In this work, the stability and error analysis are presented for fully discrete solutions of the fourth-order differential equation with the multi-term Riemann–Liouville fractional integral. Our numerical scheme is obtained by the standard central difference method in space and the formally two-step backward differentiation formula method and second-order convolution quadrature in time. Optimal order of the numerical scheme in \(L^2\)-norm is established using the discrete energy method. The analysis is supported by two numerical experiments.
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Communicated by Kai Diethelm.
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The work was supported by National Natural Science Foundation of China (11701168), Scientific Research Fund of Hunan Provincial Education Department (18B304, YB2016B033)
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Liu, Y., Yang, X., Zhang, H. et al. Analysis of BDF2 finite difference method for fourth-order integro-differential equation. Comp. Appl. Math. 40, 57 (2021). https://doi.org/10.1007/s40314-021-01449-y
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DOI: https://doi.org/10.1007/s40314-021-01449-y