分数阶Cable方程的半离散问题的稳定性与误差分析

Cable方程是模拟神经元动力学最重要的方程之一,有关该方程的研究得到了越来越多的关注.最近的研究发现,用带有分数阶导数的Cable方程来模拟神经元的动力学行为效果更好.本文旨在考察时间分数阶Cable方程的初边值问题,构造了时间分数阶Cable方程的有限差分格式.对于时间半离散格式,我们证明了格式的稳定性,并给出了误差估计式.

The Stability and Error Estimate of the Discrete Problems of Fractional Cable Equation

The cable equation has become one of the most important equations for simulating neurodynamics. The research about this equation has attracted more and more attention. Some recent developments have found that it＇s more effective to use the fractional deriva- tive cable equation to simulate the dynamic behavior of neurons. There exists a number of works concerning this equation. In particular, the numerical method has been subject of many investigations. The main work of this paper is to investigate a deformation of the time Fractional Cable equation with the initial boundary value problem,constructing the finite difference scheme of the time fractional Cable e- quation. For the time semi--discretization, we have proved the stability of the scheme and derive the error estimate.