半线性单一扰动反应-扩散问题的第四阶合网格方案.
Birtukan Tebabal Reda1, Tesfaye Aga Bullo2, Gemechis File Duressa1
1Department of Mathematics, College of Natural Science, Jimma University, Jimma, Ethiopia.
BMC research notes
|November 30, 2023
概括
本研究为半线性单一扰乱反应扩散问题引入了第四阶合网格方案,提供比现有方法更准确的解决方案.
科学领域:
- 数字分析 数字分析
- 计算数学是指计算数学.
- 应用数学 应用数学 应用数学
背景情况:
- 在各种科学和工程领域中,奇异扰乱的反应-扩散问题是常见的.
- 准确的数值解决方案对于理解这些复杂的现象至关重要.
- 对于某些问题类型,现有的方法可能缺乏足够的准确性.
研究的目的:
- 开发和介绍一个新的第四阶段装配网格方案.
- 为了提高半线性单一扰动反应扩散问题的解决方案的准确性.
- 为研究人员提供更可靠的数值工具.
主要方法:
- 准线性化技术的应用来处理半线性术语.
- 解决方案域的分离,使用一个片状均的网格.
- 有限差异近似方法将微分方程转换为差异代数方程系统.
- 使用托马斯算法的结果系统的解决方案.
主要成果:
- 拟议的方案实现了第四级准确性.
- 收分析证实了该方法的稳定性和误差极限.
- 数字示例表明,与现有方法相比,其精度更高.
- 该方案被证明适用于目标问题类.
结论:
- 开发的第四阶合网格方案有效地解决了半线性单一扰动反应-扩散问题.
- 该方法提供了更好的准确性和可靠性.
- 这项工作为该领域提供了有价值的数值技术.
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