Burgers-Fisher方程改进的交替分段Crank-Nicolson并行差分方法  

The improved alternating segment Crank-Nicolson parallel difference method for Burgers-Fisher equation

作　　者：潘悦悦 吴立飞[2] 杨晓忠[2] PAN Yue-yue;WU Li-fei;YANG Xiao-zhong(School of Control and Computer Engineering,North China Electric Power University,Beijing 102206,China;School of Mathematics and Physics,North China Electric Power University,Beijing 102206,China)

机构地区：[1]华北电力大学控制与计算机工程学院,北京102206 [2]华北电力大学数理学院,北京102206

出　　处：《高校应用数学学报（A辑）》2021年第2期193-207,共15页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家科技重大专项子课题(2017ZX07101001-01);中央高校基本科研业务费专项基金(2018MS168)。

摘　　要：Burgers-Fisher方程在气体动力学,热传导,弹性力学等领域有着广泛的应用,其快速数值解法具有重要的科学意义和工程应用价值.文中提出Burgers-Fisher方程改进的交替分段Crank-Nicolson(IASC-N)并行差分方法.IASC-N格式的构造是基于交替分段技术,将古典显式格式,隐式格式和Crank-Nicolson(C-N)格式恰当组合.理论分析了IASC-N并行差分格式解的存在唯一性,稳定性和收敛性.数值试验表明IASC-N并行差分格式线性绝对稳定,具有时间和空间二阶精度.相比串行C-N格式,IASC-N格式的计算时间能节省大约40%.说明IASC-N并行差分方法对于求解Burgers-Fisher方程是高效的.The Burgers-Fisher equation is widely used in gas dynamics,heat conduction,elastic mechanics and so on,and its fast numerical method has important scientific significance and engineering application value.In this paper,an improved alternating segment Crank-Nicolson(IASC-N)parallel difference method for Burgers-F isher equation is proposed.The construction of the IASC-N scheme is based on alternating segment technique,w hich properly combines classical explicit scheme,implicit scheme and Crank Nicolson(C-N)scheme.The existence,uniqueness,stability and convergence for the solution of the IASC-N parallel difference scheme are analyzed theoretically.Numerical experiments show that the IASC-N parallel difference scheme is linear absolute stable with second-order accuracy in time and space.Compared with the serial C-N scheme,the calculation time of IASC-N scheme can be saved about 40%.It shows that the IASC-N parallel difference method is efficient for solving Burgers-Fisher equation.

关 键 词：BURGERS-FISHER方程 IASC-N并行差分格式 线性绝对稳定性 收敛性 数值试验 

分 类 号：O241.8[理学—计算数学]