一种第四阶算术平均紧有限差异方法,用于3D平滑准变量网格网络上的非线性奇偶圆PDEs.
1Faculty of Mathematics and Computer Science, South Asian University, Maidan Garhi, New Delhi 110 068, India.
MethodsX
|October 17, 2023
概括
一种使用在准变量网格上紧离散的新数值方法有效地解决了电池模型中常见的非线性3D圆PDEs. 这种方法提供了准确的解决方案和第四阶交汇,即使对于单一模型.
科学领域:
- 数字分析 数字分析
- 计算物理 计算物理
- 应用数学 应用数学 应用数学
背景情况:
- 非线性圆局部微分方程 (PDEs) 对于模拟像电池中的对流主导的扩散等现象至关重要.
- 这些复杂模型的封闭式解决方案通常是不可用的,需要强大的数值方法.
- 现有的数值处理方法可以与单一模型和错误定位作斗争.
研究的目的:
- 引入一种新的数值方法来解决一个广泛的非线性三维圆PDEs类.
- 解决传统方法在处理单一模型和错误分散方面的局限性.
- 为分析电池扩散模型的长期和定量行为提供可靠的方法.
主要方法:
- 开发一个算术平均数的紧离谱化方案.
- 在一个准可变的电网网络上实施,只需要19个点的电网.
- 截断错误传播和网格拉伸参数效应的分析.
- 使用单调矩阵和不可归还矩阵检查收性质.
主要成果:
- 拟议的方法证明了对单一的非线性圆PDEs的适用性.
- 它有效地在整个域中分散截断错误,与固定的步骤方法不同.
- 数值分析证实了各种3D圆形PDEs的第四阶趋同.
- 像根-平均-平方误差和绝对误差等指标验证了解决方案的准确性.
结论:
- 新的数值方法为复杂的3D圆形PDEs提供了有效和准确的解决方案.
- 该方法处理单一模型和分散错误的能力提高了其在电池建模中的实用性.
- 在一个准变量的网格上,第四阶趋同意味着PDE数值分析的显著进步.
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