三维非线性神经传播方程的四阶和六阶Richardson外推法

张佳豪; 邓定文

doi:10.21656/1000-0887.450021

三维非线性神经传播方程的四阶和六阶Richardson外推法

doi: 10.21656/1000-0887.450021

张佳豪,
邓定文^,

南昌航空大学数学与信息科学学院, 南昌 330063

基金项目:

江西省杰出青年基金(20212ACB211006)；国家自然科学基金(12461070)；江西省自然科学基金重点项目(20242BAB26005)

详细信息

作者简介:
张佳豪(2000—), 男, 硕士生;邓定文(1981—), 男, 教授, 博士(通讯作者. E-mail: dengdingwen2010@163.com).

通讯作者:
邓定文(1981—), 男, 教授, 博士(通讯作者. E-mail: dengdingwen2010@163.com).

中图分类号: O357.41
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出版历程
- 收稿日期: 2024-01-27
- 修回日期: 2024-04-04
- 网络出版日期: 2025-06-30

The 4th- and 6th-Order Richardson Extrapolation Methods for Solving 3D Nonlinear Nerve Conduction Equations

ZHANG Jiahao,
DENG Dingwen^,

College of Mathematics and Information Science, Nanchang Hangkong University, Nanchang 330063, P.R.China

Funds:

The National Science Foundation of China(12461070)

摘要

摘要: 该文对一类非线性神经传播方程建立了一类交替方向隐式(ADI)紧致差分方法.其在时间上有二阶精度,在空间上有四阶精度.运用Fourier分析法和能量法可证该方法是无条件线性稳定的.此外,对这类方法,该文提出了两类Richardson外推方法,以便分别获得时、空方向均有四阶或者六阶精度的外推解,节省了计算成本.数值结果验证了该方法的精度和有效性.
- ADI法 /
- 紧致差分法 /
- Richardson外推法 /
- 稳定性
Abstract: An alternating direction implicit (ADI) compact finite difference method (CFDM) was proposed for the numerical solution of the nonlinear nerve conduction equations. The method has 2nd-order accuracy in time and 4th-order accuracy in space, respectively. With the Fourier method and the discrete energy method, the proposed method was proved to be unconditionally linearly stable. In addition, 2 kinds of Richardson extrapolation methods used along with this ADI CFDM, are also developed to get time-space numerical extrapolation solutions with 4th-order or 6th-order accuracy, respectively, and improve the computational efficiency. Numerical results verify the accuracy and efficiency of the proposed method.
- ADI method /
- compact finite difference method /
- Richardson extrapolation method /
- stability

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参考文献(26)

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三维非线性神经传播方程的四阶和六阶Richardson外推法

doi: 10.21656/1000-0887.450021

作者简介:
张佳豪(2000—), 男, 硕士生;邓定文(1981—), 男, 教授, 博士(通讯作者. E-mail: dengdingwen2010@163.com).

通讯作者:
邓定文(1981—), 男, 教授, 博士(通讯作者. E-mail: dengdingwen2010@163.com).

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The 4th- and 6th-Order Richardson Extrapolation Methods for Solving 3D Nonlinear Nerve Conduction Equations

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目录

留言板

三维非线性神经传播方程的四阶和六阶Richardson外推法

doi: 10.21656/1000-0887.450021

作者简介: 张佳豪(2000—), 男, 硕士生;邓定文(1981—), 男, 教授, 博士(通讯作者. E-mail: dengdingwen2010@163.com).

通讯作者: 邓定文(1981—), 男, 教授, 博士(通讯作者. E-mail: dengdingwen2010@163.com).

计量

出版历程

The 4th- and 6th-Order Richardson Extrapolation Methods for Solving 3D Nonlinear Nerve Conduction Equations

计量

出版历程

目录

作者简介:
张佳豪(2000—), 男, 硕士生;邓定文(1981—), 男, 教授, 博士(通讯作者. E-mail: dengdingwen2010@163.com).

通讯作者:
邓定文(1981—), 男, 教授, 博士(通讯作者. E-mail: dengdingwen2010@163.com).