一类求解非线性对流扩散方程的线性多步法  

A second-order linear multi-step method for solving nonlinear convection-diffusion equations

作　　者：张莉 罗春林 张瀚月 ZHANG Li;LUO Chun-lin;ZHANG Han-yue(VC&VR Key Lab of Sichuan Province,Sichuan Normal University,Chengdu 610066,Sichuan,China;School of Mathematical Sciences,Sichuan Normal University,Chengdu 610066,Sichuan,China)

机构地区：[1]四川师范大学可视化计算与虚拟现实四川省重点实验室,四川成都610066 [2]四川师范大学数学科学学院,四川成都610066

出　　处：《西北师范大学学报（自然科学版）》2024年第2期29-36,共8页Journal of Northwest Normal University(Natural Science)

基　　金：四川省科技计划资助项目(2022JDTD0019)。

摘　　要：研究一类非线性对流扩散方程,利用中心差商和线性多步法构造了一种新的在空间和时间上都具有二阶精度的差分格式,并利用Fourier分析和冻结系数方法分析了差分格式的稳定性,最后通过5种不同类型的数值算例验证了新方法求解非线性对流扩散方程的有效性.A new scheme is developed for the nonlinear convection-diffusion equations in this paper.Based on the central difference and linear multi-step method,the proposed scheme achieves second-order accuracy in temporal and spatial variables.By using the Fourier method and freezing coefficient method,the stability of the proposed method is analyzed.Finally,numerical results illustrate the performance of the new scheme and support the theoretical properties of the estimator.

关 键 词：非线性对流扩散方程 中心差商 线性多步法 FOURIER分析 冻结系数法 

分 类 号：O241.82[理学—计算数学]