In this paper, a θ-finite difference scheme based on cubic B-spline quasi-interpolation has been derived for the solution of time fractional Cattaneo equation. The fractional derivative of the mentioned equation has been described in the Caputo–Fabrizio sense. Time fractional derivative is approximated by a scheme of order $O({\tau }^2)$. The spatial second derivative in two consecutive time steps has been approximated using the second derivative of the cubic B-spline quasi-interpolation. For this scheme, the Fourier analysis method is used to discuss the stability and convergence. It has also been shown that the method is the convergence of order $O({\tau }^2+h^2)$. Finally, five numerical examples have been illustrated to verify the efficiency and high accuracy of the proposed scheme.

本文推导出了一种基于三次B样条拟插值的θ-有限差分格式来求解时间分数阶Cattaneo方程。已在 Caputo-Fabrizio 意义上描述了上述方程的分数阶导数。时间分数阶导数近似为阶数$哦({\tau }^2)$. 使用三次 B 样条准插值的二阶导数来近似两个连续时间步长中的空间二阶导数。对于该方案，使用傅立叶分析方法讨论稳定性和收敛性。也证明了该方法是阶次的收敛$哦({\tau }^2+H^2)$. 最后，通过五个数值算例验证了所提出方案的有效性和高精度。