Purpose

The purpose of this paper is to present a stable and efficient numerical technique based on modified trigonometric cubic B-spline functions for solving the time-fractional diffusion equation (TFDE). The TFDE has numerous applications to model many real objects and processes.

Design/methodology/approach

The time-fractional derivative is used in the Caputo sense. A modification is made in trigonometric cubic B-spline (TCB) functions for handling the Dirichlet boundary conditions. The modified TCB functions have been used to discretize the space derivatives. The stability of the technique is also discussed.

Findings

The obtained results are compared with those reported earlier showing that the present technique gives highly accurate results. The stability analysis shows that the method is unconditionally stable. Furthermore, this technique is efficient and requires less storage.

Originality/value

The current work is novel for solving TFDE. This technique is unconditionally stable and gives better results than existing results (Ford et al., 2011; Sayevand et al., 2016; Ghanbari and Atangana, 2020).

中文翻译：

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一种求解时间分数扩散方程的修正三角三次B样条搭配技术

目的

本文的目的是提出一种基于修正三角三次 B 样条函数的稳定有效的数值技术，用于求解时间分数扩散方程 (TFDE)。TFDE 有许多应用程序可以对许多真实对象和过程进行建模。

设计/方法/方法

在 Caputo 意义上使用时间分数导数。对三角三次 B 样条 (TCB) 函数进行了修改，以处理狄利克雷边界条件。修改后的 TCB 函数已被用于离散化空间导数。还讨论了该技术的稳定性。

发现

将获得的结果与之前报道的结果进行比较，表明本技术给出了高度准确的结果。稳定性分析表明该方法是无条件稳定的。此外，这种技术是有效的并且需要较少的存储。

原创性/价值

目前的工作是解决 TFDE 的新方法。这种技术是无条件稳定的，并且提供比现有结果更好的结果（Ford等，2011；Sayevand等，2016；Ghanbari 和 Atangana，2020）。