A predictor–corrector compact finite difference scheme for Burgers’ equation

In this paper, a compact predictor–corrector finite difference scheme is proposed to solve the Burgers’ equation. The scheme is based on compact derivatives approximation, by which we get the spatial approximations of first-order derivatives and second-order derivatives with fourth-order accuracy (both for inner nodes and boundary nodes). For the first time derivative item, a two-step predictor–corrector method called MacCormack method is used. Numerical experiments show the scheme is in good agreement with the exact solutions.