DQ method for initial boundary value problem of Burgers equation based on Hopf-Cole transform

Ruiping Zhang; Jiaxiang Li

doi:10.1117/12.2638872

17 May 2022 DQ method for initial boundary value problem of Burgers equation based on Hopf-Cole transform

Ruiping Zhang, Jiaxiang Li

Proceedings Volume 12259, 2nd International Conference on Applied Mathematics, Modelling, and Intelligent Computing (CAMMIC 2022); 122591Z (2022) https://doi.org/10.1117/12.2638872
Event: 2nd International Conference on Applied Mathematics, Modelling, and Intelligent Computing, 2022, Kunming, China

Abstract

The Burgers equation is transformed into a second-order linear partial differential equation by Hopf-Cole transform. Then the time variables are discretized by weighted implicit scheme, the spatial variables are discretized by cosine DQ method, and the Lagrange interpolation function is selected as the basis function, finally the implicit DQ discretization scheme for the initial boundary value problem of Burgers equation is established. The scheme has the advantages of simple mathematical principle, convenient use and less calculation and memory requirements. Numerical example shows that it has high calculation accuracy and can effectively capture physical phenomena such as shock waves. It is a competitive numerical calculation method.

Citation Download Citation

Ruiping Zhang and Jiaxiang Li "DQ method for initial boundary value problem of Burgers equation based on Hopf-Cole transform", Proc. SPIE 12259, 2nd International Conference on Applied Mathematics, Modelling, and Intelligent Computing (CAMMIC 2022), 122591Z (17 May 2022); https://doi.org/10.1117/12.2638872

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available