Convergence of Finite Difference Schemes Applied to the Cauchy Problems of Quasi-linear Partial Differential Equations of the Normal Form
Convergence of Finite Difference Schemes Applied to the Cauchy Problems of Quasi-linear Partial Differential Equations of the Normal Form
复制标题
范式拟线性偏微分方程柯西问题的有限差分格式的收敛性
DOI：
10.1007/978-981-10-6409-8_6
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发表时间：
2018
期刊：
影响因子：
--
通讯作者：
Iso Yuusuke
中科院分区：
文献类型：
--
作者：
Higashimori Nobuyuki;Fujiwara Hiroshi;Iso Yuusuke
我们在解析函数类中考虑了标准型非线性偏微分方程柯西问题。我们采用半离散有限差分近似，只对时间变量离散问题，并给出了一个关于收敛的结果。主要结果表明，相容差分格式在没有稳定性的情况下也是收敛的，从而证明了有限差分格式的稳定性与收敛之间的独立性。我们的理论结果可以在多精度算术环境下数值实现。
We consider the Cauchy problems of nonlinear partial differential equations of the normal form in the class of the analytic functions. We apply semi-discrete finite difference approximation which discretizes the problems only with respect to the time variable, and we give a result about convergence. The main result shows convergence of consistent finite difference schemes even without stability, and therefore shows independence between stability and convergence for finite difference schemes. Our theoretical result can be realized numerically on multiple-precision arithmetic environments.