This paper presents an efficient numerical technique for solving a class of time-fractional diffusion equation. The time-fractional derivative is described in the Caputo form. The L1 scheme is used for discretization of Caputo fractional derivative and a collocation approach based on sextic B-spline basis function is employed for discretization of space variable. The unconditional stability of the fully-discrete scheme is analyzed. Two numerical examples are considered to demonstrate the accuracy and applicability of our scheme. The proposed scheme is shown to be sixth order accuracy with respect to space variable and (2 − α)-th order accuracy with respect to time variable, where α is the order of temporal fractional derivative. The numerical results obtained are compared with other existing numerical methods to justify the advantage of present method. The CPU time for the proposed scheme is provided.

中文翻译：

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一类时间分数扩散方程的基于B样条的数值方法

本文提出了一种求解一类时间分数扩散方程的有效数值技术。时间分数导数以 Caputo 形式描述。Caputo分数导数的离散化采用L 1 格式，空间变量的离散化采用基于六线B样条基函数的搭配方法。分析了全离散格式的无条件稳定性。考虑两个数值例子来证明我们方案的准确性和适用性。所提出的方案被证明是关于空间变量的六阶精度和关于时间变量的 (2 -  α ) 阶精度，其中α是时间分数阶导数。将获得的数值结果与其他现有数值方法进行比较，以证明本方法的优势。提供了所提出方案的 CPU 时间。