Numerical solution of the non-linear Burgers equations using Hopf-Cole transformation

Document Type : Research Article

Authors

1 Associate Professor, Department of Mathematics, Technical and Vocational University (TVU), Tehran & Associate Professor, Department of Mathematics, Urmia University of Technology

2 Researcher, Department of Mathematics, Urmia University of Technology

Abstract

The main purpose of this article is devoted to the numerical solution of coupled one and two-dimensional non-linear Burgers equations with suitable initial and boundary conditions, by using Hopf-Cole transformation and two techniques (LFDM) and (CN-DF). In fact, using a non-linear Cole-Hope transformation the one and two-dimensional non-linear Burgers equations are reduced to diffusion equations. Then, the logarithmic finite-difference technique (LFDM) is used to discretize the diffusion equation, and the resulting equation is solved by (CN-DF) scheme. In the end, comparison of the numerical results from the change of various factors such as viscosity and the measurement of the error, the proper functioning of the numerical method and its adaptation to the analytical solution is evident.

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