KdV-Burgers方程的一类本性并行差分方法  

A Class of Difference Method with Intrinsic Parallelism for Kdv-Burgers Equation

作　　者：潘悦悦 杨晓忠[1] PAN YUEYUE;YANG XIAOZHONG(School of Mathematics and Physics,North China Electric Power University,Beijing 102206,China)

机构地区：[1]华北电力大学数理学院

出　　处：《应用数学学报》2019年第5期577-594,共18页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(No.11371135);国家科技重大专项基金(No.2017ZX07101001-01)资助项目

摘　　要：KdV-Burgers方程是非线性耗散和色散型波动方程,可以作为湍流规范方程,具有广泛的物理背景,其数值解法具有重要的科学意义和实际应用价值.针对KdV-Burgers方程,本文结合经典Crank-Nicolson格式和四个不同类型的Saul’yev非对称格式,提出了一类本性并行差分方法,构造交替分段Crank-Nicolson(ASC-N)差分格式.分析证明了ASC-N格式解的存在唯一性,线性绝对稳定性和计算精度.理论分析和数值试验结果均表明ASC-N差分格式线性绝对稳定,具有空间2阶精度,时间2阶精度(除内边界点外).在计算效率上,ASC-N格式具有明显的并行计算性质,相比较于隐式格式大幅度节省了计算时间.表明本文方法求解KdV-Burgers方程是高效可行的.The KdV-Burgers equation is a nonlinear dissipative and dispersive wave equation.It can be used as a turbulent standard equation,with a wide physical background and its numerical methods are of great scientific significance and practical application value.In view of the KdV-Burgers equation,combined with classical Crank-Nicolson scheme and four different types of Saul’yev asymmetric schemes,this paper proposes a class of difference method with intrinsic parallelism,constructing the difference scheme of Alternating Segment Crank-Nicolson(ASC-N).The existence and uniqueness,linear absolute stability and computational accuracy for the numerical solutions of the ASC-N schemes are well illustrated.Both theoretical analysis and numerical experiments show that ASC-N difference schemes are linear absolute stable,with second-order accuracy in space and second-order accuracy in time(except inner boundary points).In terms of computational efficiency,ASC-N schemes have obvious parallel computing property.Its computational time is greatly saved,compared with the implicit scheme.It is shown that the method of this paper is efficient and feasible for solving the KdV-Burgers equation.

关 键 词：KDV-BURGERS方程 本性并行 ASC-N格式 线性绝对稳定性 收敛阶 

分 类 号：O241.8[理学—计算数学]