UDC 517.958 A Brief Description of Higher-Order Accurate Numerical Solution of Burgers’ Equation T. Zhanlav∗, O. Chuluunbaatar†, V. Ulziibayar‡ ∗ Faculty of Mathematics and Computer Science National University of Mongolia, Mongolia † Laboratory of Information Technologies Joint Institute for Nuclear Research 6, Joliot-Curie str., Dubna, Moscow region, Russia, 141980 ‡ Faculty of Mathematics Mongolian University of Science and Technology P.O.Box 46/520, Ulaanbaatar, Mongolia, 210646 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 onedimensional 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. <...> Introduction We consider a one-dimensional quasi-linear parabolic partial differential equation which is known as Burgers’ equation ∂u ∂t +u∂u with an initial condition u(x, 0) = ϕ(x), a < x < b, and boundary conditions u(a, t) = f(t) and u(b, t) = g(t), t > 0, (2) (3) where ν > 0 is a coefficient of the kinematic viscosity and ϕ(x), f(t) and g(t) are known functions. <...> The Burgers’ equation can be considered as an approach to the Navier-Stokes equations [1, 2]. <...> On the other hand, the Burgers’ equation is one of a few nonlinear equations which can be solved exactly for an arbitrary initial and boundary conditions [3]. <...> However these exact solutions are impractical for the small values of viscosity constant due to a slow <...>