Excessive synchronizations of neurons in the brain networks can be a reason for some episodic disorders such as epilepsy. In this paper, we simulate neural dynamic models and their synchronizations numerically by a new numerical algorithm. In order to overcome the complexity of the problem, a suitable combination of the Legendre spectral element method and operator splitting technique is proposed to convert a complex system of partial differential equations into sparse linear algebraic systems. The simulations are explored in different aspects such as accuracy, computing the wavefront and angular speeds, computing time, the condition number of obtained algebraic systems to demonstrate the proposed scheme effectiveness. The numerical simulations and comparisons confirm the method is suitable in terms of accuracy and speed.

脑网络中神经元的过度同步可能是某些癫痫等突发性疾病的原因。在本文中，我们通过一种新的数值算法对神经动力学模型及其同步进行了数值模拟。为了克服该问题的复杂性，提出了勒让德谱元方法和算子分裂技术的适当组合，以将复杂的偏微分方程组转换为稀疏的线性代数系统。从准确性，计算波前和角速度，计算时间，获得的代数系统的条件数等不同方面对仿真进行了探讨，以证明所提出的方案的有效性。数值模拟和比较证实了该方法在准确性和速度方面都是合适的。