Numerical-analytical method for the Burgers equation

We construct an efficient numerical-analytical method for solving the initial-boundary value problem Burgers equation on a segment with periodic boundary condition. The includes reduction to linear based explicit-implicit time discretization scheme and analytical solution of auxiliary at each step using explicit form corresponding Green’s function. efficiency constructed is due fact that algorithm has only complexity in terms number spatial nodes used, without involving difference approximations derivatives desired On basis Cole-Hopf substitution, we obtain interval compare results numerical implementation this solution. developed demonstrated combination high computational accuracy result.