伯恩斯坦对一个类的Sturm-Liouville问题的拼接技术
Humaira Farzana1, Samir Kumar Bhowmik2, M A Alim3
1Department of A & S, AUST, Dhaka, 1208, Bangladesh.
Heliyon
|April 15, 2024
概括
本研究介绍了一种使用伯恩斯坦多项式的加权剩余分类方法,用于解决Sturm-Liouville问题. 该技术有效地计算正则和奇数边界值问题的固有对.
科学领域:
- 数字分析 数字分析
- 频谱理论 频谱理论
- 应用数学 应用数学 应用数学
背景情况:
- 斯图尔姆-利乌维尔问题是光谱理论和应用科学中的基本问题.
- 固有值是真实而简单的,固有函数构成希尔伯特空间基础.
- 数字解决方案对于复杂或单一的边界值问题至关重要.
研究的目的:
- 为了数值计算正则和奇数的固有对Sturm-Liouville问题.
- 开发一种使用伯恩斯坦多项式的准确和高效的计算方法.
- 为了证明加权残留合技术的适用性和优势.
主要方法:
- 在Sturm-Liouville问题上应用了加权余分合技术.
- 使用伯恩斯坦多项式在[0,1]上,以提高准确性.
- 将边界值问题转换为基于矩阵的线性代数系统,使用伯恩斯坦多项式属性和运算矩阵.
主要成果:
- 拟议的方法有效地计算了正则和单一的Sturm-Liouville问题的固有对.
- 由于其属性,伯恩斯坦多项式提供了更好的准确性和多功能性.
- 拼接技术提供了一种灵活,易于使用,条件良好的矩阵方法.
结论:
- 使用伯恩斯坦多项式的加权余分类拼接方法是解决Sturm-Liouville问题的强有力的技术.
- 该方法在各种测试案例中表现出良好的收行为和精度.
- 这种方法为光谱理论应用提供了一个计算效率高,准确的替代方案.
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