非线性Huxley扩散方程的显-隐和隐-显差分方法
首发时间:2018-04-09
摘要:扩散方程是数学物理中一类重要的偏微分法方程, 其数值解的研究有重要的理论和实际意义. 结合显式(Explicit, E)和隐式(Implicit, I)差分方法, 对非线性Huxley扩散方程构造显-隐(Explicit-Implicit, E-I)和隐-显(Implicit-Explicit, I-E)差分方法, 讨论方法数值解的存在唯一性, 稳定性和收敛性, 证明空间和时间均为2阶精度. 数值试验验证了理论分析, 表明E-I和I-E方法是无条件稳定的,并且在计算精度上相比已有的Haar wavelet格式有大幅度提高, 说明用本文方法求解非线性Huxley扩散方程是可行的.
关键词: 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; 数值实验
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The explicit-implicit and implicit-explicit difference methods for the nonlinear Huxley diffusion equation
Abstract:The diffusion equation is an important class of partial differential equations in mathematical physics, and its numerical solution has important theoretical and practical significance. In combination with the Explicit(E) and Implicit(I) difference method, the explicit-Implicit(E-I) and Implicit-Explicit(I-E) difference method are constructed for nonlinear Huxley diffusion equation. The existence and uniqueness and convergence of solutions are discussed for E-I and I-E schemes, and prove that both space and time are second-order precision. Numerical experiments verify the theoretical analysis and show that the E-I and I-E methods are unconditionally stable, and its computational accuracy is greatly improved compared to the Haar wavelet method. It shows that it is feasible to use this method to solve the nonlinear Huxley diffusion equation.
Keywords: The nonlinear Huxley diffusion equation The explicit-implicit(E-I) and implicit-explicit(I-E) difference methods Unconditional stability Order of convergence;Numerical experiments
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非线性Huxley扩散方程的显-隐和隐-显差分方法
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