The objective of this paper is to present an efficient numerical technique for solving time fractional modified anomalous subdiffusion equation. Anomalous diffusion equation has its role in various branches of biological sciences. B-spline is a piecewise function to draw curves and surfaces, which maintain its degree of smoothness at the connecting points. B-spline provides an active process of approximation to the limit curve. In current attempt, B-spline curve is used to approximate the solution curve of time fractional modified anomalous subdiffusion equation. The process is kept simple involving collocation procedure to the data points. The time fractional derivative is approximated with the discretized form of the Riemann-Liouville derivative. The process results in the form of system of algebraic equations, which is solved using a variant of Thomas algorithm. In order to ensure the convergence of the procedure, a valid method named Von Neumann stability analysis is attempted. The graphical and tabular display of results for the illustrated examples is presented, which stamped the efficiency of the proposed algorithm.

中文翻译：

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修正分数异常次扩散方程解的B样条新变体

本文的目的是提出一种求解时间分数阶修正异常子扩散方程的有效数值技术。反常扩散方程在生物科学的各个分支中都有其作用。B-spline 是一种分段函数，用于绘制曲线和曲面，在连接点处保持其平滑度。B 样条提供了一个主动逼近极限曲线的过程。在目前的尝试中，B-样条曲线用于近似时间分数修正异常子扩散方程的解曲线。该过程保持简单，涉及到数据点的搭配过程。时间分数阶导数近似于黎曼-刘维尔导数的离散形式。该过程以代数方程组的形式出现，这是使用 Thomas 算法的变体解决的。为了保证过程的收敛性，尝试了一种名为冯诺依曼稳定性分析的有效方法。给出了所示示例结果的图形和表格显示，这标志着所提出算法的效率。