Discrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational Science2658-46702658-7149Peoples' Friendship University of Russia8256Research ArticleA Brief Description of Higher-Order Accurate Numerical Solution of Burgers’ EquationZhanlavTFaculty of Mathematics and Computer Sciencetzhanlav@yahoo.comChuluunbaatarOLaboratory of Information Technologieschuka@jinr.ruUlziibayarVFaculty of Mathematicsv.ulzii@yahoo.comNational University of Mongolia, MongoliaJoint Institute for Nuclear ResearchMongolian University of Science and Technology150120141869108092016Copyright © 2014,2014Two 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.Burgers’ equationhigher-order accurate numerical solutionуравнение Бюргерсаповышенной точности численного решения