A Brief Description of Higher-Order Accurate Numerical Solution of Burgers’ Equation

Cover Page
  • Authors: Zhanlav T1, Chuluunbaatar O2, Ulziibayar V3
  • Affiliations:
    1. National University of Mongolia, Mongolia
    2. Joint Institute for Nuclear Research
    3. Mongolian University of Science and Technology
  • Issue: No 1 (2014)
  • Pages: 86-91
  • Section: Articles
  • URL: http://journals.rudn.ru/miph/article/view/8256
  • Cite item

Abstract


Two new higher-order accurate finite-difference schemes for the numerical solution of boundary-value problem of the Burgers’ equation are suggested. Burgers equation is a one-dimensional analogue of the Navier-Stokes equations describing the dynamics of fluids and it possesses all of its mathematical properties. Besides the Burgers’ equation, one of the few nonlinear partial differential equations which has the exact solution, and it can be used as a test model to compare the properties of different numerical methods. A first scheme is purposed for the numerical solution of the heat equation. It has a sixth-order approximation in the space variable, and a third-order one in the time variable. A second scheme is used for finding a numerical solution for the Burgers’s equation using the relationship between the heat and Burgers’ equations. This scheme also has a sixth-order approximation in the space variable. The numerical results of test examples are found in good agreement with exact solutions and confirm the approximation orders of the schemes proposed.

About the authors

T Zhanlav

National University of Mongolia, Mongolia

Email: tzhanlav@yahoo.com
Faculty of Mathematics and Computer Science

O Chuluunbaatar

Joint Institute for Nuclear Research

Email: chuka@jinr.ru
Laboratory of Information Technologies

V Ulziibayar

Mongolian University of Science and Technology

Email: v.ulzii@yahoo.com
Faculty of Mathematics

References

Statistics

Views

Abstract - 42

PDF (English) - 42

Cited-By



Copyright (c) 2014 Жанлав Т., Чулуунбаатар О., Улзийбаяр В.

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

This website uses cookies

You consent to our cookies if you continue to use our website.

About Cookies