时间/时空分数阶Cable方程在神经元树突棘反常扩散模拟中有着非常重要的意义，对于其高精度、高效率的求解也成为现代科学计算的重要问题之一。本项目拟结合区域分解算法和正交样条配置方法来研究时间/时空分数阶Cable方程，研究内容包括以下两个方面：(1)基于正交样条配置方法，构造模型的全离散格式，建立其稳定性和收敛性理论，并通过带权指数衰减误差估计和Hardy不等式推导出模型的长时间估计; (2)针对问题所产生的几乎块对角线性系统，结合区域分解策略，给出并行求解算法，并通过数值算例验证方法的可行性以及理论分析的准确性。本项目的预期成果不仅能丰富时间/时空分数阶Cable方程的数值模拟算法以及误差分析理论，还将扩大正交样条配置方法的应用范围，并有望解决某些实际问题，如石油渗流、地下水污染等，具有重要的理论意义和应用价值。

Time/Time-Space fractional Cable equations have a very important significance for modelling the anomalous diffusion of dendritic spines in neurons, and how to design the high-precision and high-efficiency algorithm is one of important problems in modern scientific computing. This project will combine the domain decomposition algorithm and orthogonal spline collocation method to study time/time-space fractional Cable equations, and the contents include two parts as follows: (1) Based on orthogonal spline collocation method, we propose the full-discretization formula, establish the theory of stability and convergence, and provide the long-time error estimates by the exponential decay error estimate with weight and Hardy inequality; (2) For the almost block diagonal system, combing domain decomposition method, we propose the parallel algorithm and verify the practicability of scheme and the effectiveness of theoretical analysis by numerical examples. The expected results of the project will not only enrich the numerical algorithm and error estimate theory of time/time-space fractional Cable equation, but also widen the application scope of the orthogonal spline collocation method, and hope to solve some practical applications, for example, oil seepage, ground water pollution and so on, which are significant to the theoretical research and practical applications.