摘要
非线性反应-扩散-对流方程,广泛存在于化学工程,传热传质和水质污染等领域中,其数值解法具有重要的科学意义和工程应用价值。针对一类非线性反应-扩散-对流方程,本文提出一类显式和隐式交替差分方法,基于交替技术将时间网格点按照奇偶划分,联合使用古典显格式和隐格式,构造出显隐交替差分格式和隐显交替差分格式。理论分析得出显隐交替差分方法的解是存在唯一的、线性稳定的和线性收敛的。数值试验验证了理论分析,试验显示显隐交替格式与隐显交替格式相较于隐格式节省约23%的计算效率,表明本文方法求解非线性反应-扩散-对流方程是有效的。
Nonlinear reaction-diffusion-convection equation is widely used in chemical engineering,heat and mass transfer,water pollution and other fields.Its numerical solution has important scientific significance and engineering application value.For a class of nonlinear reaction-diffusionconvection equation,this paper proposes a class of explicit and implicit alternating difference method.Based on the alternating technique,the time grid points are divided according to odd and even,and the classical explicit scheme and implicit scheme are combined.The explicit implicit alternating difference scheme and implicit explicit alternating difference scheme are constructed.The theoretical analysis shows that the solution of the explicit implicit alternative difference method is unique,linearly stable and linearly convergent.The numerical experiments verify the theoretical analysis.The experimental results show that the explicit implicit alternative scheme and the implicit explicit alternative scheme save about 23%computational efficiency compared with the implicit scheme,which shows that the proposed method is effective for solving the nonlinear reaction-diffusion-convection equation.
作者
吴吉明
李嘉正
杨晓忠
WU Jiming;LI Jiazheng;YANG Xiaozhong(School of Mathematics and Physics,North China Electric Power University,Beijing102206,China;Engineering Ecology and Nonlinear Science Research Center,North China Electric Power University,Beijing102206,China)
出处
《内蒙古大学学报（自然科学版）》
CAS
北大核心
2021年第4期354-364,共11页
Journal of Inner Mongolia University：Natural Science Edition
基金
国家科技重大专项子课题(2017ZX07101001-01)
国家自然科学基金(11371135)。
关键词
非线性反应-扩散-对流方程
显隐交替差分
线性稳定性
线性收敛性
数值试验
nonlinear reaction-diffusion-convection equation
explicit implicit alternating difference
linear stability
linear convergence
numerical experiment
