Iterated Crank–Nicolson Runge–Kutta Methods and Their Application to Wilson–Cowan Equations and Electroencephalography Simulations
Year: 2024
Type: article
Abstract: The Wilson–Cowan model has been widely applied for the simulation of electroencephalography (EEG) waves associated with neural activities in the brain. The Runge–Kutta (RK) method is commonly used to numerically solve the Wilson–Cowan equations. In this paper, we focus on enhancing the accuracy of the numerical method by proposing a strategy to construct a class of fourth-order RK methods using a generalized iterated Crank–Nicolson procedure, where the RK coefficients depend on a free parameter c2. When c2 is set to 0.5, our method becomes a special case of the classical fourth-order RK method. We apply the proposed methods to solve the Wilson–Cowan equations with two and three neuron populations, modeling EEG epileptic dynamics. Our simulations demonstrate that when c2 is set to 0.4, the proposed RK4-04 method yields smaller errors compared to those obtained using the classical fourth-order RK method. This is particularly visible when the spectral radius of the connection matrix or the excitation-inhibition coupling coefficient is relatively large.
Source: Foundations
Authors: Jinjie Liu, Qi Lu, Hacene Boukari, Fatima Boukari
Institution: Delaware State University
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,137
Awards: Excellence in Research: Optical Studies of Nanoparticles and Biomacromolecules in Complex Biopolymeric Systems, G3115553707, G3150754229, Delaware INBRE, CISE-MSI: DP: III: Training and Partnership in Data Science for Advancing Research in Biomolecular Detection, G8048591340, G8429442293, G8803126937, G9000093202
OpenAlex ID: W4404321871