四川师范大学学报（自然科学版）2017，Vol.40Issue(2)：177-183,7.DOI:10.3969/j.issn.1001-8395.2017.02.006
求解波动方程的2种显式高精度紧致差分格式
Two Kinds of Explicit High Order Compact Difference Schemes for Solving Wave Equations
摘要
Abstract
In this paper,an explicit compact difference scheme is obtained for solving the one dimensional wave equation.The truncation error of the scheme is O(τ2 + h4).It's constructed by applying the fourth-order accurate Padé approximation in space and the second-order accurate central difference in time.Then,the remainder of the truncation error correction method is employed to improve the accuracy of the discretization of time,the truncation error of the improved scheme is O(τ4 + τ2 h2 + h4),which means the scheme has an overall fourth-order accuracy.And then,the stability conditions of the two schemes are obtained by the Fourier method.Finally,the accuracy and the reliability of the present two schemes are verified by numerical experiments.关键词
波动方程/Padé逼近/紧致格式/显式差分/稳定性Key words
wave equation/Padéapproximation/compact scheme/explicit difference/stability分类
数理科学引用本文复制引用
姜蕴芝,葛永斌..求解波动方程的2种显式高精度紧致差分格式[J].四川师范大学学报（自然科学版）,2017,40(2):177-183,7.基金项目
国家自然科学基金(11361045) （11361045）
宁夏大学自然科学基金项目(ZR1407)和宁夏大学研究生创新项目(GIP2016032)对本文给予了资助,谨致谢意. （ZR1407）
