修正等宽方程数值解的高阶精确混合技术

IF 2.1 3区 物理与天体物理 Q2 ACOUSTICS
Emre Kirli , Serpil Cikit
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引用次数: 0

摘要

本文采用一种高阶精确混合技术,建立了用于定义孤立波的修正等宽方程的近似解。空间积分采用三次b样条和四阶紧凑有限差分(FOCFD)格式,时间积分采用四阶龙格-库塔(RK4)格式。在目前的技术中,利用FOCFD格式构造了新的空间二阶导数近似,其中未知量的空间二阶导数可以用未知量本身及其一阶导数表示。因此,空间二阶导数达到了四阶的精度,而在标准三次b样条中则用二阶的精度表示。利用特征值的概念讨论了该方法的稳定性。对三个测试问题进行了检验,以验证所建议技术的有效性和适用性。计算结果与前人的数值结果进行了比较。结果表明,该混合方法具有精度高、计算量小的优点。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A high order accurate hybrid technique for numerical solution of modified equal width equation
In this present study, a high-order accurate hybrid technique is developed to establish the approximate solution of Modified Equal Width (MEW) equation which is used to define solitary waves. The spatial integration is based on combining the cubic B-spline and a fourth-order compact finite-difference (FOCFD) scheme , while the temporal integration is carried out by using fourth-order Runge–Kutta (RK4) scheme. In present technique, the new approximation for the spatial second derivative is constructed by the FOCFD scheme in which the spatial second derivatives of unknowns can be written in terms of the unknowns themselves and their first derivatives. Hence, the spatial second derivative reaches the accuracy of order four, while it is represented by the accuracy of order two in the standard cubic B-spline. The stability of the suggested technique is discussed by using the concept of eigenvalue. Three test problems are examined to verify the efficiency and applicability of the suggested technique. The computed results are compared with the other numerical results in previous works. The comparisons reveal that the suggested hybrid technique provides better results with high accuracy and minimum computational effort.
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来源期刊
Wave Motion
Wave Motion 物理-力学
CiteScore
4.10
自引率
8.30%
发文量
118
审稿时长
3 months
期刊介绍: Wave Motion is devoted to the cross fertilization of ideas, and to stimulating interaction between workers in various research areas in which wave propagation phenomena play a dominant role. The description and analysis of wave propagation phenomena provides a unifying thread connecting diverse areas of engineering and the physical sciences such as acoustics, optics, geophysics, seismology, electromagnetic theory, solid and fluid mechanics. The journal publishes papers on analytical, numerical and experimental methods. Papers that address fundamentally new topics in wave phenomena or develop wave propagation methods for solving direct and inverse problems are of interest to the journal.
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