Linearized Implicit Numerical Method for Burgers’ Equation

Nonlinear engineering: Modeling and application

article

Vijitha Mukundan¹  Ashish Awasthi¹ 

[1] Department of Mathematics, National Institute of Technology

关键词: Burgers’ equation;    Kinematic viscosity;    Method of lines;    Linearization;    Implicit finite difference method;    Taylor series;   

DOI  :  10.1515/nleng-2016-0031

来源: De Gruyter

【 摘 要 】

In this work, a novel numerical scheme based on method of lines (MOL) is proposed to solve the nonlinear time dependent Burgers’ equation. The Burgers’ equation is semi discretized in spatial direction by using MOL to yield system of nonlinear ordinary differential equations in time. The resulting system of nonlinear differential equations is integrated by an implicit finite difference method. We have not used Cole-Hopf transformation which gives less accurate solution for very small values of kinematic viscosity. Also, we have not considered nonlinear solvers that are computationally costlier and take more running time.In the proposed scheme nonlinearity is tackled by Taylor series and the use of fully discretized scheme is easy and practical. The proposed method is unconditionally stable in the linear sense. Furthermore, efficiency of the proposed scheme is demonstrated using three test problems.

【 授权许可】

Unknown