  In this work, high order splitting methods have been used for calculating the
numerical solutions of the Burgers' equation in one space dimension with
periodic and Dirichlet boundary conditions. However, splitting methods with
real coefficients of order higher than two necessarily have negative
coefficients and can not be used for time-irreversible systems, such as Burgers
equations, due to the time-irreversibility of the Laplacian operator.
Therefore, the splitting methods with complex coefficients and extrapolation
methods with real and positive coefficients have been employed. If we consider
the system as the perturbation of an exactly solvable problem(or can be easily
approximated numerically), it is possible to employ highly efficient methods to
approximate Burgers' equation. The numerical results show that the methods with
complex time steps having one set of coefficients real and positive, say
$a_i\in\mathbb{R}^+$ and $b_i\in\mathbb{C}^+$, and high order extrapolation
methods derived from a lower order splitting method produce very accurate
solutions of the Burgers' equation.
