A nonconventional stability approach for a nonlinear Crank–Nicolson method solving degenerate Kawarada problems
A nonconventional stability approach for a nonlinear Crank–Nicolson method solving degenerate Kawarada problems
复制标题
解决退化 Kawarada 问题的非线性 Crank-Nicolson 方法的非常规稳定性方法
DOI：
10.1016/j.aml.2023.108730
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发表时间：
2023
影响因子：
3.7
通讯作者：
Torres, Eduardo Servin
中科院分区：
文献类型：
--
作者：
Sheng, Qin;Torres, Eduardo Servin
传统上，非线性Kawarada问题的有限差分近似的数值稳定性仅通过冻结源项来显示，即忽略了淬火非线性的潜在危害。这种方法即使在局部稳定性分析的意义上也留下了不足之处。本文对基础方程的非线性源项在不冻结的情况下的数值稳定性进行了改进分析。所实现的策略可以扩展到类似的高维情况。包括仿真实验。
Conventionally, the numerical stability of finite difference approximations of nonlinear Kawarada problems is shown only via frozen source terms, that is, ignoring potential jeopardization from quenching nonlinearities. The approach leaves an inadequacy behind even in the sense of localized stability analysis. This paper provides a much improved analysis of the numerical stability without freezing nonlinear source terms of the underlying equations. The strategy implemented can be extended for similar endeavors to higher dimensional cases. Simulation experiments are included.