High Accuracy Numerical Method For The Fractional Cable Equation

Fractional differential equations have been widely applied in many scienceand engineering fields, such as physics chemistry, biology and so on. For exam-ple, the fractional cable equation has become one of the important equations toanalogue neurodynamics. Therefore, the algorithm research for fractional differ-ential equations has important significance.In this paper, we propose a computationally effcient numerical techniqueto approximate the fractional cable equation. An improved implicit numeri-cal method with high accuracy is proposed. The error analysis is given. As0 <γ₁,γ₂≤0.5850, the stability of the numerical method is got by the Fourieranalysis method. Numerical example shows that the numerical method is effec-tive.