广义神经传播方程的Wilson元收敛性分析  

Convergence Analysis of Wilson Element for a Generalized Nerve Conduction Equation

作　　者：梁聪刚 张厚超 石东洋 LIANG Conggang;ZHANG Houchao;SHI Dongyang(School of Mathematics and Statistics,Pingdingshan University,Pingdingshan 467000,Henan;School of Mathematics and Statistics,Zhengzhou University,Zhengzhou 450052,Henan)

机构地区：[1]平顶山学院数学与统计学院,河南平顶山467000 [2]郑州大学数学与统计学院,河南郑州450052

出　　处：《四川师范大学学报（自然科学版）》2020年第2期212-218,共7页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(11271340和11671369);河南省科技计划项目(162300410082)。

摘　　要：利用Wilson元对一类广义神经传播方程提出了新的半离散和全离散逼近格式.基于单元的性质,通过定义新的双线性型,在不需要插值后处理技术的前提下,分别得到了比传统的H^1-范数更大的模意义下相应的O(h^2)和O(h^2+τ^2)阶的误差分析结果,比通常的估计高出一阶.这里,h、τ分别表示空间剖分参数和时间步长.In this paper,using Wilson element,new semi-discrete and fully-discrete schemes are proposed for a generalized nerve conduction equation.With the norm stronfer than H′-norm,the corwergence results with order O(h^2)and O(h^2+τ^2)for the primitive solwtion are obtaincd for the corresponding schemes,respettively,where h andτare parameters of subdivision in space and tine step,rospectively.The above results,based on the properties of the element and by defining a nwe bilinear form,are just one order higher than the usual error estimates for wilson element without using the technique of extrapolation and interpolated postpro cessing.

关 键 词：广义神经传播方程 WILSON元 半离散和全离散格式 收敛性 

分 类 号：O242.21[理学—计算数学]