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

ZHANG Jiahao; DENG Dingwen

doi:10.21656/1000-0887.450021

Volume 46 Issue 6

Jun. 2025

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Article Navigation > Applied Mathematics and Mechanics > 2025 > 46(6): 800-808

ZHANG Jiahao, DENG Dingwen. The 4th- and 6th-Order Richardson Extrapolation Methods for Solving 3D Nonlinear Nerve Conduction Equations[J]. Applied Mathematics and Mechanics, 2025, 46(6): 800-808. doi: 10.21656/1000-0887.450021

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

doi: 10.21656/1000-0887.450021

ZHANG Jiahao,
DENG Dingwen^,

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

Received Date: 2024-01-27
Rev Recd Date: 2024-04-04
Publish Date: 2025-06-01

Abstract

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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References(26)

References

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