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Higher-Order Numerical Solution of Two-Dimensional Coupled Burgers’ Equations
Institute of Mathematics, National University of Mongolia, Ulaanbaatar, Mongolia
Joint Institute for Nuclear Research, Moscow, Russia
School of Applied Sciences, Mongolian University of Science and Technology, Ulaanbaatar, Mongolia
- 1 Institute of Mathematics, National University of Mongolia, Ulaanbaatar, Mongolia
- 2 Joint Institute for Nuclear Research, Moscow, Russia
- 3 School of Applied Sciences, Mongolian University of Science and Technology, Ulaanbaatar, Mongolia
American Journal of Computational Mathematics·Volume 06 (2016)·Pages 120–129·Published 27 April 2016·DOI10.4236/ajcm.2016.62013
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Abstract
We proposed a higher-order accurate explicit finite-difference scheme for solving the two-dimensional heat equation. It has a fourth-order approximation in the space variables, and a second-order approximation in the time variable. As an application, we developed the proposed numerical scheme for solving a numerical solution of the two-dimensional coupled Burgers’ equations. The main advantages of our scheme are higher accurate accuracy and facility to implement. The good accuracy of the proposed numerical scheme is tested by comparing the approximate numerical and the exact solutions for several two-dimensional coupled Burgers’ equations.
KeywordsTwo-Dimensional Coupled Burgers’ EquationHopf-Cole TransformationHigher-Order Accurate Numerical Schemes
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