Nonlinear stability of reaction-diffusion equations using wavelet-like incremental unknowns
Nonlinear stability of reaction-diffusion equations using wavelet-like incremental unknowns
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DOI：
10.1016/j.apnum.2012.12.003
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发表时间：
2013-06
影响因子：
2.8
通讯作者：
Lunji Song;Yujiang Wu
中科院分区：
文献类型：
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作者：
Lunji Song;Yujiang Wu
提出了不同类型的增量未知量作为在有限差分离散背景下发展数值格式的一种手段。本文提出了一种求解具有多项式非线性的二维反应扩散方程的类小波型增量未知数方法，并验证了增量未知数方法的小，且具有L2正交分解的性质。给出了基于WIU的欧拉显式和半隐式格式。并导出了相应的稳定性条件，改善了相应经典算法在多层网格中的稳定性约束。给出了反应扩散方程的数值结果，展示了WIU的特征。
Incremental unknowns of different types were proposed as a means to develop numerical schemes in the context of finite difference discretizations. In this article, we present a novel wavelet-like incremental unknowns (WIU) method for the two-dimensional reaction–diffusion equations with a polynomial nonlinearity, and verify that the WIU is small as expected and it has the property of L2orthogonal decomposition. Euler explicit and semi-implicit schemes based on the WIU are presented. And sufficient stability conditions are derived to improve the stability constraints of the corresponding classical algorithms in the multilevel meshes. Numerical results of reaction–diffusion equations are given to exhibit the features of the WIU.