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非线性Huxley扩散方程的显-隐和隐-显差分方法

发表时间:2019-03-22  浏览量:465  下载量:24
全部作者: 高迪,杨晓忠
作者单位: 华北电力大学数理学院
摘 要: 非线性Huxley扩散方程是数学物理中一类重要的偏微分方程,对其数值解的研究具有重要的理论价值和实际意义。研究结合显式(explicit)差分格式和隐式(implicit)差分格式,对非线性Huxley扩散方程分别构造显-隐(explicit-implicit,E-I)差分格式和隐-显(implicit-explicit,I-E)差分格式,理论分析给出了E-I差分格式和I-E差分格式数值解的存在唯一性、稳定性和收敛性,证明了空间和时间均为2阶精度。数值试验验证了理论分析,表明E-I差分格式和I-E差分格式是无条件稳定的,并在计算精度上相比已有的Haar wavelet格式有大幅度的提高,说明使用本文构造的E-I差分格式和I-E差分格式求解非线性Huxley扩散方程是可行的。
关 键 词: 计算数学;非线性Huxley扩散方程;显-隐(E-I)和隐-显(I-E)差分方法;无条件稳定性;收敛阶;数值试验
Title: Explicit-implicit and implicit-explicit difference methods for the nonlinear Huxley diffusion equation
Author: GAO Di, YANG Xiaozhong
Organization: School of Mathematics and Physics, North China Electric Power University
Abstract: The nonlinear Huxley diffusion equation is an important class of partial differential equations in mathematical physics, and its numerical solution has important theoretical value and practical significance. In combination with the explicit and implicit difference schemes, the explicit-implicit (E-I) and implicit-explicit (I-E) difference schemes are respectively constructed for nonlinear Huxley diffusion equation. The existence and uniqueness, stability, and convergence of numerical solutions are discussed for E-I and I-E difference schemes, proving that both space and time are second-order precision. Numerical experiments verify the theoretical analysis and show that the E-I and I-E difference schemes are unconditionally stable, and its computational accuracy is greatly improved compared to the existing Haar wavelet scheme. It explains that it is feasible to use the E-I and I-E difference schemes to solve the nonlinear Huxley diffusion equation.
Key words: computational mathematics; nonlinear Huxley diffusion equation; explicit-implicit (E-I) and implicit-explicit (I-E) difference methods; unconditional stability; order of convergence; numerical experiment
发表期数: 2019年2月第1期
引用格式: 高迪,杨晓忠. 非线性Huxley扩散方程的显-隐和隐-显差分方法[J]. 中国科技论文在线精品论文,2019,12(1):7-17.
 
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