Numerical Solution and Stability Analysis for a Class of Nonlinear Differential Equations

被引：0
作者：
Ying Li
Yong Wang
机构：
[1] Harbin Institute of Technology,School of Mathematics
来源：
International Journal of Theoretical Physics | 2021年 / 60卷
关键词：
Stability; Partial differential equation; Numerical errors;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, one-dimensional Burgers equation and one-dimensional Laval nozzle flow Euler equation are numerically solved, and the stability of the numerical solutions is analyzed theoretically. In order to satisfy the stability of the numerical solution, the explicit MacCormack scheme is used to obtain the stable solution of the computer numerical simulation. In addition, the numerical and analytical solutions of the Euler equation for one-dimensional Laval nozzle flow are compared, and the results are completely consistent, which verifies the correctness of the numerical solution.
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页码：2573 / 2582
页数：9
相关论文
共 27 条
[1]  
Choudhary MK(2004)Mathematical modeling of heat transfer, condensation, and cappilary flow in porous insulation on a cold pipe Int. J. Heat Mass Transfer 47 5629-5638
[2]  
Karki KC(1997)Modeling convection/diffusion processes in porous textiles with inclusion of humidity-dependent air permeability Int. Commun. Heat Mass Transfer 24 709-724
[3]  
Patankar SV(2012)Unconditionally stable difference methods for delay partial differential equations Numer. Math. 3 579-601
[4]  
Gibsona PW(2020)Random attractors for locally monotone stochastic partial differential equations J. Diff. Eq. 269 3414-3455
[5]  
Charmchib M(2012)Burgers’ equation and the sticky particles model J. Math. Phys. 6 063709-199
[6]  
Huang CM(1984)mathematical model illustrating the theory of turbulence Adv. Appl. Mech. 1 171-495
[7]  
Vandewalle S(2006)A finite volume scheme for nonlinear parabolic equations derived from one-dimensional local Dirichlet problems Numer. Math. 102 463-1177
[8]  
Gess B(1978)Stability and convergence of finite difference methods for systems of nonlinear reactiondiffusion equations SIAM J. Numer. Anal. 15 1161-904
[9]  
Liu W(2005)numerical solution of Burgers equation by finite element method constructed on the method of discretization in time Appl. Math. Comput 170 895-2564
[10]  
Schenke A(2010)Soliton and numerical solutions of the Burgers equation and comparing them Int. J. Math. Anal. 4 2547-2590
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