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极坐标系下求解一维Helmholtz方程的六阶紧致差分方法

Compact Sixth-order Finite Difference Scheme for Solving 1D Helmholtz Equation in Polar Coordinates
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摘要 基于极坐标系下四阶紧致差分方法,运用Taylor级数展开构造了一种极坐标系下求解一维Helmholtz方程的六阶紧致差分方法,通过分析所构造差分格式的截断误差确保该方法在理论上可达到六阶精度,最后通过数值算例验证了所构造差分格式的精确性和可靠性. Based on the fourth order finite difference method,a sixth-order compact finite difference scheme which aims to solve one dimensional Helmholtz equation in Polar coordinates is put forward by applying Taylor series.The sixth-order accuracy of this method can be confirmed in theory by analyzing truncation error of the constructed difference scheme.And the accuracy and efficiency of the proposed method is validated through the numerical examples.
作者 苏晓璐 冯秀芳
机构地区 宁夏大学数学计算机学院
出处 《宁夏大学学报（自然科学版）》 CAS 2016年第2期153-156,160,共5页 Journal of Ningxia University(Natural Science Edition)
基金 国家自然科学基金资助项目(11161036 11361045)
关键词 HELMHOLTZ方程 紧致差分方法 极坐标 Helmholtz equation compact finite difference schemes polar coordinates
分类号 O241.82 [理学—计算数学]
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参考文献8

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二级参考文献13

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宁夏大学学报（自然科学版）
2016年 第2期

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