In this paper, we formulated the finite difference method for the fourth order integro-differential equation with the Riemann-Liouville multi-term fractional integral kernels. The formally two-step backward differentiation formula method and second-order convolution quadrature are used in time. The and -norm stability and convergence at each time level are given. Numerical results show that our scheme obtains the expected optimal convergence rates.

中文翻译：

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具有多项 RL 分数积分核的四阶方程的 BDF2 FDM

在本文中，我们用 Riemann-Liouville 多项分数积分核构造了四阶积分微分方程的有限差分方法。形式上的两步向后微分公式方法和二阶卷积求积及时使用。给出了每个时间级别的和-范数稳定性和收敛性。数值结果表明，我们的方案获得了预期的最优收敛速度。