Analysis of a numerical method improves stability and efficiency in multi-dimensional cable equations, indicating potential advances in modeling ionic motion.
The time fractional cable equation (TFCE) extends the classical cable model to describe the anomalous diffusion of ionic motion in the nervous system. This paper presents an efficient numerical method for solving the TFCE, combining the orthogonal spline collocation (OSC) method with the alternating direction implicit (ADI) method for spatial discretization. For time discretization, it employs a second‐order backward differentiation formula (BDF2) along with the classical L1 approximation for the Caputo fractional derivative. The stability and convergence of the proposed method are rigorously analyzed. Finally, numerical experiments validate the theoretical results and demonstrate its accuracy and efficiency.
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Wang et al. (2025) studied this question.
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