参数均的有限差分配方,无振荡,通过指数分线来解决异常扰乱的延迟抛物线微分方程
Zerihun Ibrahim Hassen1, Gemechis File Duressa2
1Department of Mathematics, Arba Minch University, Arba Minch, Ethiopia. zerihunibrahim@gmail.com.
使用指数分线的新数值方法有效地解决了异常扰乱的抛物线对流-扩散问题. 这种无振荡的方法确保稳定和均的融合解决方案,即使有边界层.
科学领域:
- 数字分析 数字分析
- 计算数学 计算数学 计算数学
- 部分微分方程 部分微分方程
背景情况:
- 奇异扰乱的依赖时间的延迟抛物线对流-扩散问题往往表现出边界层.
- 传统的数值方法在这些边界层的坡和振荡中扎,导致不准确的解决方案.
- 开发强大的数值方案对于准确模拟这些复杂现象至关重要.
研究的目的:
- 为特定类别的异常扰动问题开发一种无振荡,参数均的数值方法.
- 为了应对解决方案中边界层和的梯度所带来的挑战.
- 为具有这些特性的问题提供可靠的计算工具.
主要方法:
- 一种混合方法,将时间方向上的隐性欧勒法和空间方向上的指数分线法结合起来.
- 引入一个指数拟合因子来管理扰动参数的影响.
- 采用统一的网格来实现空间的分密化.
主要成果:
- 开发的数值方案显示稳定性和统一的错误估计.
- 该方法在最大规范中实现线性顺序的均收.
- 数字示例证实了理论发现和拟议方案的有效性.
结论:
- 拟议的指数拟合线方法为单一扰乱的依赖时间的延迟抛物线对流-扩散问题提供了有效和准确的解决方案.
- 该方法成功地处理了没有振荡的边界层行为.
- 这种技术提供了一个可靠的替代传统方法的问题与的坡度.
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